You searched for subject:(Automatic differentiation).
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University of Waterloo
1.
Embaye, Samuel.
The determination of structured Hessian matrices via automatic differentiation.
Degree: 2014, University of Waterloo
URL: http://hdl.handle.net/10012/8850 
► In using automatic differentiation (AD) for Hessian computation, efficiency can be achieved by exploiting the sparsity existing in the derivative matrix. However, in the case…
(more)
▼ In using automatic differentiation (AD) for Hessian computation, efficiency can be achieved by exploiting the sparsity existing in the derivative matrix. However, in the case where the Hessian is dense, this cannot be done and the space requirements to compute the Hessian can become very large. But if the underlying function can be expressed in a structured form, a “deeper” sparsity can be exploited to minimize the space requirement. In this thesis, we provide a summary of automatic differentiation (AD) techniques, as applied to Jacobian and Hessian matrix determination, as well as the graph coloring techniques involved in exploiting their sparsity. We then discuss how structure in the underlying function can be used to greatly improve efficiency in gradient/Jacobian computation. We then propose structured methods for Hessian computation that substantially reduce the space required. Finally, we propose a method for Hessian computation where the structure of the function is not provided.
Subjects/Keywords: automatic differentiation; structure; gradient; Hessian
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APA (6th Edition):
Embaye, S. (2014). The determination of structured Hessian matrices via automatic differentiation. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/8850
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Embaye, Samuel. “The determination of structured Hessian matrices via automatic differentiation.” 2014. Thesis, University of Waterloo. Accessed January 28, 2020.
http://hdl.handle.net/10012/8850.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Embaye, Samuel. “The determination of structured Hessian matrices via automatic differentiation.” 2014. Web. 28 Jan 2020.
Vancouver:
Embaye S. The determination of structured Hessian matrices via automatic differentiation. [Internet] [Thesis]. University of Waterloo; 2014. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/10012/8850.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Embaye S. The determination of structured Hessian matrices via automatic differentiation. [Thesis]. University of Waterloo; 2014. Available from: http://hdl.handle.net/10012/8850
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Toronto
2.
Paige, Cody.
Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver.
Degree: 2013, University of Toronto
URL: http://hdl.handle.net/1807/35661
► The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward…
(more)
▼ The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward mode ADjoint is a combination of an adjoint sensitivity analysis method with a forward mode automatic differentiation (AD) and is a modification of the reverse mode ADjoint method proposed by \citet{Mader:2008:B}. A colouring acceleration technique is presented to reduce the computational cost increase associated with forward mode AD. The forward mode AD facilitates the implementation of the laminar Navier – Stokes (NS) equations. The forward mode ADjoint method is applied to a three-dimensional computational fluid dynamics solver. The resulting Euler and viscous ADjoint sensitivities are compared to the reverse mode Euler ADjoint derivatives and a complex-step method to demonstrate the reduced computational cost and accuracy. Both comparisons demonstrate the benefits of the colouring method and the practicality of using a forward mode AD.
MAST
Advisors/Committee Members: Martins, Joaquim R. R. A., Aerospace Science and Engineering.
Subjects/Keywords: Laminar Navier-Stokes; adjoint; automatic differentiation; 0538
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APA (6th Edition):
Paige, C. (2013). Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/35661
Chicago Manual of Style (16th Edition):
Paige, Cody. “Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver.” 2013. Masters Thesis, University of Toronto. Accessed January 28, 2020.
http://hdl.handle.net/1807/35661.
MLA Handbook (7th Edition):
Paige, Cody. “Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver.” 2013. Web. 28 Jan 2020.
Vancouver:
Paige C. Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver. [Internet] [Masters thesis]. University of Toronto; 2013. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/1807/35661.
Council of Science Editors:
Paige C. Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver. [Masters Thesis]. University of Toronto; 2013. Available from: http://hdl.handle.net/1807/35661
University of Arizona
3.
Chernikov, Dmitry.
PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance
.
Degree: 2017, University of Arizona
URL: http://hdl.handle.net/10150/626368
► In this dissertation we investigate methods of solving various optimization problems with PDE constraints, i.e. optimization problems that have a system of partial differential equations…
(more)
▼ In this dissertation we investigate methods of solving various optimization problems with PDE constraints, i.e. optimization problems that have a system of partial differential equations in the set of constraints, and develop frameworks for a number of practically inspired problems that were not considered in the literature before. Such problems arise in areas like fluid mechanics, chemical engineering, finance, and other areas where a physical system needs to be optimized. In most of the literature sources on PDE-constrained optimization only relatively simple systems of PDEs are considered, they are either linear, or the size of the system is small. On the contrary, in our case, we search for solution methods to problems constrained by large (8 to 10 equations) and non-linear systems of PDEs. More specifically, in the first part of the dissertation we consider a multiphysics phenomenon where electromagnetic and mechanical fields interact within an electrically conductive body, and develop the optimization framework to find an efficient way to control one field through another. We also apply the developed PDE-constrained optimization framework to a financial options portfolio optimization problem, and more specifically consider the case that to the best of our knowledge is not covered in the literature.
Advisors/Committee Members: Krokhmal, Pavlo (advisor), Zhupanska, Olesya (advisor), Krokhmal, Pavlo (committeemember), Zhupanska, Olesya (committeemember), Zhang, Hao (committeemember), Furfaro, Roberto (committeemember).
Subjects/Keywords: adjoint differentiation;
automatic differentiation;
multiphysics;
nonlinear optimization;
optimization of portfolio of options;
PDE-constrained optimization
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APA (6th Edition):
Chernikov, D. (2017). PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance
. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/626368
Chicago Manual of Style (16th Edition):
Chernikov, Dmitry. “PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance
.” 2017. Doctoral Dissertation, University of Arizona. Accessed January 28, 2020.
http://hdl.handle.net/10150/626368.
MLA Handbook (7th Edition):
Chernikov, Dmitry. “PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance
.” 2017. Web. 28 Jan 2020.
Vancouver:
Chernikov D. PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance
. [Internet] [Doctoral dissertation]. University of Arizona; 2017. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/10150/626368.
Council of Science Editors:
Chernikov D. PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance
. [Doctoral Dissertation]. University of Arizona; 2017. Available from: http://hdl.handle.net/10150/626368
Virginia Tech
4.
Alexe, Mihai.
Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems.
Degree: PhD, Computer Science, 2011, Virginia Tech
URL: http://hdl.handle.net/10919/37515
► Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes…
(more)
▼ Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the
solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the
differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This dissertation develops a complete framework for fully discrete adjoint sensitivity analysis and inverse problem solutions, in the context of time dependent, adaptive mesh, and adaptive step models. The discrete framework addresses all the necessary ingredients
of a stateâ ofâ theâ art adaptive inverse solution algorithm: adaptive mesh and time step refinement, solution grid transfer operators, a priori and a posteriori error analysis and estimation, and discrete adjoints for sensitivity analysis of fluxâ limited numerical algorithms.
Advisors/Committee Members: Sandu, Adrian (committeechair), Ribbens, Calvin J. (committee member), Cao, Yang (committee member), De Sturler, Eric (committee member), Borggaard, Jeffrey T. (committee member).
Subjects/Keywords: Inverse problems; Adjoint Method; Adaptive Mesh Refinement; Automatic Differentiation
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APA (6th Edition):
Alexe, M. (2011). Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/37515
Chicago Manual of Style (16th Edition):
Alexe, Mihai. “Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems.” 2011. Doctoral Dissertation, Virginia Tech. Accessed January 28, 2020.
http://hdl.handle.net/10919/37515.
MLA Handbook (7th Edition):
Alexe, Mihai. “Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems.” 2011. Web. 28 Jan 2020.
Vancouver:
Alexe M. Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems. [Internet] [Doctoral dissertation]. Virginia Tech; 2011. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/10919/37515.
Council of Science Editors:
Alexe M. Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems. [Doctoral Dissertation]. Virginia Tech; 2011. Available from: http://hdl.handle.net/10919/37515
University of Waterloo
5.
Koppel, Leonid.
On the Manifold: Representing Geometry in C++ for State Estimation.
Degree: 2018, University of Waterloo
URL: http://hdl.handle.net/10012/14264
► Manipulating geometric objects is central to state estimation problems in robotics. Typical algorithms must optimize over non-Euclidean states, such as rigid transformations on the SE(3)…
(more)
▼ Manipulating geometric objects is central to state estimation problems in robotics. Typical algorithms must optimize over non-Euclidean states, such as rigid transformations on the SE(3) manifold, and handle measurements expressed in multiple coordinate frames. Researchers typically rely on C++ libraries for geometric tasks. Commonly used libraries range from linear algebra software such as Eigen to robotics-targeted optimization frameworks such as GTSAM, which provides manifold operations and automatic differentiation of arbitrary expressions. This thesis examines how geometric operations in existing software can be improved, both in runtime performance and in the expression of geometric semantics, to support rapid and error-free development of robotics algorithms.
This thesis presents wave_geometry, a C++ manifold geometry library providing representations of objects in affine, Euclidean, and projective spaces, and the Lie groups SO(3) and SE(3). It encompasses the main contributions of this work: an expression template-based automatic differentiation system and compile-time checking of coordinate frame semantics. The library can evaluate Jacobians of geometric expressions in forward and reverse mode with little runtime overhead compared to hand-coded derivatives, and exceeds the performance of existing libraries. While high performance is achieved by taking advantage of compile-time knowledge, the library also provides dynamic expressions which can be composed at runtime.
Coordinate frame conversions are a common source of mistakes in calculations.
However, the validity of operations can automatically be checked by tracking the coordinate frames associated with each object. A system of rules for propagating coordinate frame semantics though geometric operations, including manifold operations, is developed. A template-based method for checking coordinate frame semantics at compile time, with no runtime overhead, is presented.
Finally, this thesis demonstrates an application to state estimation, presenting a framework for formulating nonlinear least squares optimization problems as factor graphs. The framework combines wave_geometry expressions with the widely used Ceres Solver software, and shows the utility of automatically differentiated geometric expressions.
Subjects/Keywords: robotics; computer vision; manifold geometry; software tools; automatic differentiation; coordinate frames
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APA (6th Edition):
Koppel, L. (2018). On the Manifold: Representing Geometry in C++ for State Estimation. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/14264
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Koppel, Leonid. “On the Manifold: Representing Geometry in C++ for State Estimation.” 2018. Thesis, University of Waterloo. Accessed January 28, 2020.
http://hdl.handle.net/10012/14264.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Koppel, Leonid. “On the Manifold: Representing Geometry in C++ for State Estimation.” 2018. Web. 28 Jan 2020.
Vancouver:
Koppel L. On the Manifold: Representing Geometry in C++ for State Estimation. [Internet] [Thesis]. University of Waterloo; 2018. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/10012/14264.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Koppel L. On the Manifold: Representing Geometry in C++ for State Estimation. [Thesis]. University of Waterloo; 2018. Available from: http://hdl.handle.net/10012/14264
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Utah State University
6.
Hodson, Joshua D.
Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio.
Degree: PhD, Mechanical and Aerospace Engineering, 2019, Utah State University
URL: https://digitalcommons.usu.edu/etd/7574
► This work focuses on the development of efficient methods for wing shape optimization for morphing wing technologies. Existing wing shape optimization processes typically rely…
(more)
▼ This work focuses on the development of efficient methods for wing shape optimization for morphing wing technologies. Existing wing shape optimization processes typically rely on computational fluid dynamics tools for aerodynamic analysis, but the computational cost of these tools makes optimization of all but the most basic problems intractable. In this work, we present a set of tools that can be used to efficiently explore the design spaces of morphing wings without reducing the fidelity of the results significantly. Specifically, this work discusses
automatic differentiation of an aerodynamic analysis tool based on lifting line theory, a light-weight gradient-based optimization framework that provides a parallel function evaluation capability not found in similar frameworks, and a modification to the lifting line equations that makes the analysis method and optimization process suitable to wings of arbitrary aspect ratio. The toolset discussed is applied to several wing shape optimization problems. Additionally, a method for visualizing the design space of a morphing wing using this toolset is presented. As a result of this work, a light-weight wing shape optimization method is available for analysis of morphing wing designs that reduces the computational cost by several orders of magnitude over traditional methods without significantly reducing the accuracy of the results.
Advisors/Committee Members: Douglas F. Hunsaker, Robert E. Spall, Barton L. Smith, ;.
Subjects/Keywords: aerodynamics; optimization; automatic differentiation; lifting line theory; aspect ratio
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APA ·
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APA (6th Edition):
Hodson, J. D. (2019). Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio. (Doctoral Dissertation). Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/7574
Chicago Manual of Style (16th Edition):
Hodson, Joshua D. “Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio.” 2019. Doctoral Dissertation, Utah State University. Accessed January 28, 2020.
https://digitalcommons.usu.edu/etd/7574.
MLA Handbook (7th Edition):
Hodson, Joshua D. “Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio.” 2019. Web. 28 Jan 2020.
Vancouver:
Hodson JD. Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio. [Internet] [Doctoral dissertation]. Utah State University; 2019. [cited 2020 Jan 28].
Available from: https://digitalcommons.usu.edu/etd/7574.
Council of Science Editors:
Hodson JD. Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio. [Doctoral Dissertation]. Utah State University; 2019. Available from: https://digitalcommons.usu.edu/etd/7574
University of Illinois – Urbana-Champaign
7.
Ghosh, Alexander.
Multi-CubeSat mission planning enabled through parallel computing.
Degree: PhD, 4048, 2013, University of Illinois – Urbana-Champaign
URL: http://hdl.handle.net/2142/45554
► Small CubeSat-class satellites are opening up new avenues for science and technology development within the space industry. What was once a purely educational tool has…
(more)
▼ Small CubeSat-class satellites are opening up new avenues for science and technology development within the space industry. What was once a purely educational tool has quickly become the newest international exploration platform for low earth orbit missions. These sub-10 kg satellites ride into space as tertiary payloads, kicked out of their launch vehicles after all other satellites have reached their target orbit, and are left to survive in whatever ride-share provided orbit they are deposited into. Due to their small mass and volume, it has been infeasible until very recently to put any form of on-board propulsion on these spacecraft without a significant sacrifice of the science objectives. Current research at the University of Illinois and other institutions will soon lead to the flight of CubeSat-class low thrust, low-power, yet low-specific impulse propellant systems. This technology should enable CubeSats to acquire new orbits from their launch positions, to rendezvous and dock together, or to reconfigure their constellations within orbit. Because of the atypical combination of low-thrust with high propellant mass consumption, a new toolset is needed to assist with planning of both single and cooperative multi-satellite missions.
This work contributes a new framework for the calculation of high-fidelity trajectories in low Earth orbit. A shooting method is reformulated as a non-linear programming problem, and wrapped by a novel mesh refinement algorithm, which updates the time discretization based on a cumulative thrust density function. The states are propagated using a higher order explicit Dormand-Prince integrator with an error-adaptive step size. The necessary derivatives and Jacobian are developed in real time using algorithmic
differentiation, which allows for significantly higher accuracy over traditional finite difference methods. This framework is tested against analytical methods developed by Wiesel for in-plane, and Edelbaum and Kechichian for out of plane, and is shown to match or surpass their results.
This work further contributes to the field by developing an extended framework that allows the simultaneous integration of multiple satellites using parallel processing on a super computer, and lays out the necessary constraints to define cooperative intercept, rendezvous and orbit reconfiguration problems.
Finally, this dissertation develops a new approach to parallel algorithmic
differentiation, allowing the concurrent calculation of multiple derivatives in a user-transparent manner, simultaneously while propagating multiple satellites. This is accomplished by using a Cartesian processor grid and a new parallel communication scheme to maintain the most data locality per processor, enabling orders of magnitude speedup by comparison to both serial, and the previously developed parallel processing approach.
This new parallel algorithmic
differentiation technique is demonstrated with a series of test cases, developing cooperative maneuvers for from two to four satellites experiencing…
Advisors/Committee Members: Coverstone, Victoria L. (advisor), Coverstone, Victoria L. (Committee Chair), Conway, Bruce A. (committee member), Burton, Rodney L. (committee member), Swenson, Gary R. (committee member).
Subjects/Keywords: satellite; trajectory; trajectory optimization; optimization; cubesat; picosatellite; earth orbit; Orbit; low thrust; low-thrust; automatic differentiation; algorithmic differentiation; parallel processing
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APA (6th Edition):
Ghosh, A. (2013). Multi-CubeSat mission planning enabled through parallel computing. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45554
Chicago Manual of Style (16th Edition):
Ghosh, Alexander. “Multi-CubeSat mission planning enabled through parallel computing.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 28, 2020.
http://hdl.handle.net/2142/45554.
MLA Handbook (7th Edition):
Ghosh, Alexander. “Multi-CubeSat mission planning enabled through parallel computing.” 2013. Web. 28 Jan 2020.
Vancouver:
Ghosh A. Multi-CubeSat mission planning enabled through parallel computing. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/2142/45554.
Council of Science Editors:
Ghosh A. Multi-CubeSat mission planning enabled through parallel computing. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45554
8.
Sällberg, Gustav.
Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions.
Degree: Faculty of Science & Engineering, 2015, Linköping UniversityLinköping University
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090
► The master thesis is focused on how a local volatility surfaces can be extracted by optimization with respectto smoothness and price error. The pricing…
(more)
▼ The master thesis is focused on how a local volatility surfaces can be extracted by optimization with respectto smoothness and price error. The pricing is based on utility based pricing, and developed to be set in arisk neutral pricing setting. The pricing is done in a discrete multinomial recombining tree, where the timeand price increments optionally can be equidistant. An interpolation algorithm is used if the option that shallbe priced is not matched in the tree discretization. Power utility functions are utilized, where the log-utilitypreference is especially studied, which coincides with the (Kelly) portfolio that systematically outperforms anyother portfolio. A fine resolution of the discretization is generally a property that is sought after, thus a seriesof derivations for the implementation are done to restrict the computational encumbrance and thus allow finer discretization. The thesis is mainly focused on the derivation of the method rather than finding optimal parameters thatgenerate the local volatility surfaces. The method has shown that smooth surfaces can be extracted, whichconsider market prices. However, due to lacking available interest and dividend data, the pricing error increasessymmetrically for longer option maturities. However, the method shows exponential convergence and robustnessto different initial (flat) volatilities for the optimization initiation. Given an optimal smooth local volatility surface, an arbitrary payoff function can then be used to price thecorresponding option, which could be path-dependent, such as barrier options. However, only vanilla optionswill be considered in this thesis. Finally, we find that the developed
Subjects/Keywords: local volatility surface; LVS; optimization; roughness; smooth; risk neutral pricing; optimal growth; pricing error; automatic differentiation; algorithmic differentiation
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APA (6th Edition):
Sällberg, G. (2015). Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions. (Thesis). Linköping UniversityLinköping University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Sällberg, Gustav. “Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions.” 2015. Thesis, Linköping UniversityLinköping University. Accessed January 28, 2020.
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Sällberg, Gustav. “Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions.” 2015. Web. 28 Jan 2020.
Vancouver:
Sällberg G. Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions. [Internet] [Thesis]. Linköping UniversityLinköping University; 2015. [cited 2020 Jan 28].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Sällberg G. Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions. [Thesis]. Linköping UniversityLinköping University; 2015. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Oxford
9.
Birkisson, Asgeir.
Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework.
Degree: PhD, 2013, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533
► Ordinary differential equations (ODEs) play an important role in mathematics. Although intrinsically, the setting for describing ODEs is the continuous framework, where differential operators are…
(more)
▼ Ordinary differential equations (ODEs) play an important role in mathematics. Although intrinsically, the setting for describing ODEs is the continuous framework, where differential operators are considered as maps from one function space to another, common numerical algorithms for ODEs discretise problems early on in the solution process. This thesis is about continuous analogues of such discrete algorithms for the numerical solution of ODEs. This thesis shows how Newton's method for finite dimensional system can be generalised to function spaces, where it is known as Newton-Kantorovich iteration. It presents affine invariant damping strategies for increasing the chance of convergence for the Newton-Kantorovich iteration. The derivatives required in this continuous setting are Fréchet derivatives, the continuous analogue of Jacobian matrices. In this work, we present how automatic differentiation techniques can be applied to compute Fréchet derivatives. We introduce chebop, a Matlab solver for nonlinear boundary-value problems, which combines damped Newton iteration in function space and automatic Fréchet differentiation. By proving that affine operators have constant Fréchet derivatives, it is demonstrated how automatic linearity detection of computed quantities can be implemented. This is valuable for black-box solvers, which can use the information to determine whether an iteration scheme has to be employed for solving a problem. Like nonlinear systems of equations, nonlinear boundary-value problems can have multiple solutions. This thesis present two techniques for obtaining multiple solutions of operator equations: deflation and path-following. An algorithm combining the two techniques is proposed.
Subjects/Keywords: 515; Mathematics; Numerical analysis; Ordinary differential equations; nonlinear boundary value problems; automatic differentiation; Frechet derivatives; Chebfun; automatic linearity detection; deflation
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APA (6th Edition):
Birkisson, A. (2013). Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533
Chicago Manual of Style (16th Edition):
Birkisson, Asgeir. “Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework.” 2013. Doctoral Dissertation, University of Oxford. Accessed January 28, 2020.
http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533.
MLA Handbook (7th Edition):
Birkisson, Asgeir. “Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework.” 2013. Web. 28 Jan 2020.
Vancouver:
Birkisson A. Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework. [Internet] [Doctoral dissertation]. University of Oxford; 2013. [cited 2020 Jan 28].
Available from: http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533.
Council of Science Editors:
Birkisson A. Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework. [Doctoral Dissertation]. University of Oxford; 2013. Available from: http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533
Ohio University
10.
Heller, Richard.
Checkpointing without operating system intervention:
Implementing Griewank's algorithm.
Degree: MS, Electrical Engineering & Computer Science
(Engineering and Technology), 1998, Ohio University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831
Checkpointing without operating system
intervention: Implementing Griewank's
algorithm
Advisors/Committee Members: Juedes, David (Advisor).Subjects/Keywords: Griewank's Algorithm; Automatic Differentiation; LogAD Compiler
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MLA ·
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CSE |
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APA (6th Edition):
Heller, R. (1998). Checkpointing without operating system intervention:
Implementing Griewank's algorithm. (Masters Thesis). Ohio University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831
Chicago Manual of Style (16th Edition):
Heller, Richard. “Checkpointing without operating system intervention:
Implementing Griewank's algorithm.” 1998. Masters Thesis, Ohio University. Accessed January 28, 2020.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831.
MLA Handbook (7th Edition):
Heller, Richard. “Checkpointing without operating system intervention:
Implementing Griewank's algorithm.” 1998. Web. 28 Jan 2020.
Vancouver:
Heller R. Checkpointing without operating system intervention:
Implementing Griewank's algorithm. [Internet] [Masters thesis]. Ohio University; 1998. [cited 2020 Jan 28].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831.
Council of Science Editors:
Heller R. Checkpointing without operating system intervention:
Implementing Griewank's algorithm. [Masters Thesis]. Ohio University; 1998. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831
University of Illinois – Chicago
11.
Yoffe, Genady.
Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving.
Degree: 2012, University of Illinois – Chicago
URL: http://hdl.handle.net/10027/9116
► Solving polynomial systems by homotopy continuation consists of two stages: we first define a family of systems, the homotopy, and then we track the solution…
(more)
▼ Solving polynomial systems by homotopy continuation consists of two stages: we first define a family of systems, the homotopy, and then we track the solution paths defined by the homotopy. Tracking all paths is a pleasingly parallel computation. The problem we consider in this thesis is tracking one solution path when use of extended precision is required. While tracking only one solution path could occur for systems of larger dimensions and degrees, as it is no longer feasible to compute all solutions, the need to track one difficult path with multiprecision arithmetic often arises for bigger systems. The main
subject of this thesis is compensating for the extra cost of double double (DD) and of quad double (QD) precision in path tracking for sparse polynomial systems of moderate sizes by employing multiple cores. First we obtained a scalable multithreaded DD/QD version of Newton's method and subsequently of a path tracker. We achieved on eight cores for moderate systems close to maximal speedups in quad double path tracking. It appeared that in dimensions in which our DD/QD multithreaded path tracker achieves good speedups, with the use of some widely accepted algorithms for sparse polynomial systems, which we originally integrated into our multithreaded path tracker and its input processing procedure, both the path tracking and input processing take an unacceptably long time. Subsequently we have greatly increased the efficiency of our multithreaded implementation in working dimensions by improvements in three different directions. First we suggested a new input processing procedure based on functionality of a Standard Template Library (STL) sorted associative container. Secondly we came up with a choice of much more suitable predictor. Thirdly we integrated into our multithreaded implementation a prudent algorithm for polynomial evaluation and differentiation, which is based on the ideas of reverse mode
Automatic Differentiation (AD). Recently we efficiently accelerated with general purpose graphics unit the same AD-like algorithm for polynomial evaluation and differentiation. We obtained two digit speedups for moderate systems as hardware double arithmetic is used.
Advisors/Committee Members: Verschelde, Jan (advisor), Friedland, Shmuel (committee member), Leykin, Anton (committee member), Nicholls, David (committee member), Turan, Gyorgy (committee member).
Subjects/Keywords: Multithreaded; Graphics Processing Unit; Compute Unified Device Architecture; Automatic Differentiation; GPU; CUDA; AD
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CSE |
Export
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APA (6th Edition):
Yoffe, G. (2012). Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/9116
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Yoffe, Genady. “Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving.” 2012. Thesis, University of Illinois – Chicago. Accessed January 28, 2020.
http://hdl.handle.net/10027/9116.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Yoffe, Genady. “Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving.” 2012. Web. 28 Jan 2020.
Vancouver:
Yoffe G. Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving. [Internet] [Thesis]. University of Illinois – Chicago; 2012. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/10027/9116.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Yoffe G. Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving. [Thesis]. University of Illinois – Chicago; 2012. Available from: http://hdl.handle.net/10027/9116
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Linköping University
12.
Hjelmberg, David.
Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation.
Degree: Production Economics, 2014, Linköping University
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875
► In this master thesis we have examined the possibility of pricing multiple American options, on an underlying asset with discrete dividends, with a finite…
(more)
▼ In this master thesis we have examined the possibility of pricing multiple American options, on an underlying asset with discrete dividends, with a finite difference method. We have found a good and stable way to price one American option by solving the BSM PDE backwards, while also calculating the Greeks of the option with automatic differentiation. The list of Greeks for an option is quite extensive since we have been using a local volatility surface. We have also tried to find a way to price several American options simultaneously by solving a forward PDE. Unfortunately, we haven't found any previous work that we could use with our local volatility surface, while still keeping down the computational time. The closest we got was to calculate the value of a compound option in a forward mode, but in order to use this to value an American option, we needed to go through an iterative process which calculated a forward or backward European PDE in every step.
Subjects/Keywords: American options; BSM PDE; discrete dividends; forward PDE; local volatility surface; automatic differentiation
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APA ·
Chicago ·
MLA ·
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CSE |
Export
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APA (6th Edition):
Hjelmberg, D. (2014). Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation. (Thesis). Linköping University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Hjelmberg, David. “Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation.” 2014. Thesis, Linköping University. Accessed January 28, 2020.
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Hjelmberg, David. “Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation.” 2014. Web. 28 Jan 2020.
Vancouver:
Hjelmberg D. Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation. [Internet] [Thesis]. Linköping University; 2014. [cited 2020 Jan 28].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Hjelmberg D. Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation. [Thesis]. Linköping University; 2014. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Ohio University
13.
Kang, Yixiu.
Implementation of Forward and Reverse Mode Automatic
Differentiation for GNU Octave Applications.
Degree: MS, Electrical Engineering & Computer Science
(Engineering and Technology), 2003, Ohio University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867
► In this work, we present two C/C++ implementations of general purpose automatic differentiation (AD) for GNU Octave applications: FAD for forward mode AD and…
(more)
▼ In this work, we present two C/C++
implementations of general purpose
automatic differentiation (AD)
for GNU Octave applications: FAD for forward mode AD and LogAD for
reverse mode AD with bisection checkpointing. Both FAD and LogAD
accept functions written in the GNU Octave language and work in the
Octave environment via dynamically linked functions. FAD evaluates
the product of the Jacobian of the input function and an arbitrary
vector in time and space that are proportional to the time and
space used by the original function. LogAD evaluates the product of
an arbitrary vector and the Jacobian of the input function via a
checkpointing approach first proposed by Griewank in
1992.
Advisors/Committee Members: Juedes, David (Advisor).
Subjects/Keywords: Computer Science; Automatic Differentiation (AD); Forward Mode Automatic Differentiation; Reverse Mode Automatic Differentiation; Checkpointing; Scientific Computing; Computational Mathematics
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kang, Y. (2003). Implementation of Forward and Reverse Mode Automatic
Differentiation for GNU Octave Applications. (Masters Thesis). Ohio University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867
Chicago Manual of Style (16th Edition):
Kang, Yixiu. “Implementation of Forward and Reverse Mode Automatic
Differentiation for GNU Octave Applications.” 2003. Masters Thesis, Ohio University. Accessed January 28, 2020.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867.
MLA Handbook (7th Edition):
Kang, Yixiu. “Implementation of Forward and Reverse Mode Automatic
Differentiation for GNU Octave Applications.” 2003. Web. 28 Jan 2020.
Vancouver:
Kang Y. Implementation of Forward and Reverse Mode Automatic
Differentiation for GNU Octave Applications. [Internet] [Masters thesis]. Ohio University; 2003. [cited 2020 Jan 28].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867.
Council of Science Editors:
Kang Y. Implementation of Forward and Reverse Mode Automatic
Differentiation for GNU Octave Applications. [Masters Thesis]. Ohio University; 2003. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867
Universidade do Rio Grande do Sul
14.
Espath, Luis Felipe da Rosa.
Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos.
Degree: 2013, Universidade do Rio Grande do Sul
URL: http://hdl.handle.net/10183/85033
► Neste trabalho buscou-se consolidar aspectos referentes à otimização de problemas envolvidos na mecânica dos meios contínuos, envolvendo diferentes áreas do conhecimento, tais como: otimização matemática,…
(more)
▼ Neste trabalho buscou-se consolidar aspectos referentes à otimização de problemas envolvidos na mecânica dos meios contínuos, envolvendo diferentes áreas do conhecimento, tais como: otimização matemática, diferenciação automática, análise estrutural, análise aerodinâmica, parametrização de curvas, superfícies e sólidos do tipo B-spline racionais não-uniformes (NURBS, acrônimo do inglês), análise IsoGeométrica (IGA, acrônimo do inglês) e análise por Elementos Finitos (FEA, acrônimo do inglês). Como objetivo final busca-se otimizar formas de cascas estruturais e formas de corpos aerodinâmicos imersos em escoamentos compressíveis. No que concerne à análise estrutural, esta é realizada via análise IsoGeométrica utilizando elementos sólidos para modelar cascas. Uma cinemática co-rotacional abrangente e precisa baseada na exata decomposição polar é desenvolvida, para lidar com problemas estáticos e dinâmicos altamente não lineares. Na análise estática foram implementados o método de Newton-Raphson e controle de deslocamentos generalizado, para problemas dinâmicos foram implementados o método -generalizado (G ) e o método energia momento generalizado (GEMM+ ). A análise aerodinâmica é realizada via análise por Elementos Finitos para modelar escoamentos compressíveis viscosos e não viscosos em regimes transônicos e supersônicos. Um esquema característico baseado na separação da equação de momento (CBS, acrônimo do inglês) é utilizado para obter uma adequada integração temporal. No que concerne à otimização matemática, é utilizado um método baseado em gradientes, conhecido por programação quadrática sequencial (SQP, acrônimo do inglês), onde a avaliação as derivadas de Fréchet são levadas a cabo via diferenciação automática (AD, acrônimo do inglês). No que concerne aos resultados finais é realizada a otimização estrutural de forma de cascas modeladas como sólidos são apresentados, evidenciando um desempenho ótimo com respeito à energia de deformação interna. Os resultados de otimização aerodinâmica bidimensionais apresentam perfis aerodinâmicos ótimos com respeito à relação arrasto/sustentação para uma ampla gama de número de Mach, enquanto um resultado tridimensional é apresentado evidenciando a robustez e eficiência da implementação proposta. Pretendese estabelecer com este trabalho as bases para pesquisas em problemas de otimização aeroelástica.
Consolidation of the link among optimization problems in continuum mechanics, involving different fields, such as mathematical optimization, automatic differentiation, structural analysis, aerodynamic analysis, curves, surfaces and solids parameterization using Non Uniform Rational B-spline (NURBS), IsoGeometric Analysis (IGA), Finite Element Analysis (FEA) is looked for. Structural shape optimization of shell structures and aerodynamic shape optimization of immersed bodies in compressible flows are the main goals of this work. Concerning structural analysis, the so-called IsoGeometric analysis is employed. An accurate and comprehensive corotational kinematic based on the…
Advisors/Committee Members: Awruch, Armando Miguel.
Subjects/Keywords: Mathematical optimization; Estruturas (Engenharia); Structural IsoGeometric analysis; Mecânica do contínuo; Otimização matemática; Aerodynamic finite element analysis; Elementos finitos; NURBS; Automatic differentiation
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Espath, L. F. d. R. (2013). Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/85033
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Espath, Luis Felipe da Rosa. “Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos.” 2013. Thesis, Universidade do Rio Grande do Sul. Accessed January 28, 2020.
http://hdl.handle.net/10183/85033.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Espath, Luis Felipe da Rosa. “Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos.” 2013. Web. 28 Jan 2020.
Vancouver:
Espath LFdR. Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2013. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/10183/85033.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Espath LFdR. Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos. [Thesis]. Universidade do Rio Grande do Sul; 2013. Available from: http://hdl.handle.net/10183/85033
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Colorado
15.
Dunham, Benjamin Zane.
High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.
Degree: PhD, 2017, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/228
► This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common…
(more)
▼ This work presents a new
automatic differentiation method, Nilpotent Matrix
Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions – most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series – without changing data-type or modifying code line by line; this allows
differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed “stencils,” each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the “forward mode” is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of <i>N</i> – i.e., <i>O</i>(1) – the <i>N</i> × <i>N</i> Hessian can be found in <i>O</i>(<i>N</i>) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive – e.g., a <i>N</i> × <i>N</i> × <i>N</i> rank-three tensor can be found in <i>O</i>(<i>N</i>
2). Alternatively, a Hessian-vector product can be found in <i>O</i>(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step
differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics.
Advisors/Committee Members: Kurt K. Maute, Ryan P. Starkey, Alireza Doostan.
Subjects/Keywords: adjoint; automatic differentiation; complex step; hessian-vector; linear algebra; nilpotent element; Aerospace Engineering; Applied Mathematics; Mathematics
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Dunham, B. Z. (2017). High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/228
Chicago Manual of Style (16th Edition):
Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 28, 2020.
https://scholar.colorado.edu/asen_gradetds/228.
MLA Handbook (7th Edition):
Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Web. 28 Jan 2020.
Vancouver:
Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2020 Jan 28].
Available from: https://scholar.colorado.edu/asen_gradetds/228.
Council of Science Editors:
Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/asen_gradetds/228
University of Colorado
16.
Dunham, Benjamin Zane.
High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.
Degree: PhD, 2017, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/167
► This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common…
(more)
▼ This work presents a new
automatic differentiation method, Nilpotent Matrix
Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions – most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series – without changing data-type or modifying code line by line; this allows
differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed “stencils,” each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error.
Although this use of the method in the “forward mode” is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with
N inputs and an adjoint solver whose cost is independent of
N – i.e.,
O(1) – the
N ×
N Hessian can be found in
O(
N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive – e.g., a
N ×
N ×
N rank-three tensor can be found in
O(
N2). Alternatively, a Hessian-vector product can be found in
O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step
differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics.
Advisors/Committee Members: Kurt K. Maute, Ryan P. Starkey, Alireza Doostan, Brian M. Argrow, Bengt Fornberg.
Subjects/Keywords: adjoint; automatic differentiation; complex step; Hessian-vector; linear algebra; nilpotent element; Aerospace Engineering; Applied Mathematics; Mathematics
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Record Details
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Dunham, B. Z. (2017). High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/167
Chicago Manual of Style (16th Edition):
Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 28, 2020.
https://scholar.colorado.edu/asen_gradetds/167.
MLA Handbook (7th Edition):
Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Web. 28 Jan 2020.
Vancouver:
Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2020 Jan 28].
Available from: https://scholar.colorado.edu/asen_gradetds/167.
Council of Science Editors:
Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/asen_gradetds/167
17.
Martin, Nathan.
Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology.
Degree: Docteur es, Mathematiques Appliquees, 2013, Toulouse, INSA
URL: http://www.theses.fr/2013ISAT0021
► Un certain nombre d’écoulements géophysiques, tels que les écoulements de glace ou de lave magmatique, impliquent le mouvement gravitaire à faible nombre de Reynolds d’un…
(more)
▼ Un certain nombre d’écoulements géophysiques, tels que les écoulements de glace ou de lave magmatique, impliquent le mouvement gravitaire à faible nombre de Reynolds d’un fluide viscoplastique à surface libre sur un socle rocheux. Leur modélisation fait apparaître des lois de comportement rhéologique et des descriptions de leurs intéractions avec le socle rocheux qui reposent sur des paramétrisations empiriques. Par ailleurs, l’observation systématique de ce type d’écoulements avec une grande précision est rarement possible ; les données associées à l’observation de ces écoulements, principalement des données de surface (télédétections), peuvent être peu denses, manquantes ou incertaines. Elles sont aussi le plus souvent indirectes : des paramètres inconnus comme le glissement basal ou la rhéologie sont difficilement mesurables in situ.Ce travail de thèse s’attache à la modélisation directe et inverse de ces écoulements géophysiques, particulièrement les écoulements de glace, par des méthodes variationnelles à travers la résolution du problème de Stokes pour les fluides en loi de puissance.La méthode de résolution du problème direct (Stokes non-linéaire) repose sur le principe du minimum de dissipation qui mène à un problème variationnel de type point-selle à quatre champs pour lequel on montre l’existence de solutions. La condition d’incompressibilité et la loi de comportement représentent alors des contraintes associées au problème de minimisation. La recherche des points critiques du lagrangien correspondant est réalisée à l’aide d’un algorithme de type lagrangien augmenté, discrétisé par éléments finis triangles à trois champs. Cet algorithme conduit à un important gain tant en temps de calcul qu’en utilisation mémoire par rapport aux algorithmes classiques.On s’intéresse ensuite à la modélisation numérique inverse de ces fluides à l’aide du modèle adjoint et des deux principaux outils associés : l’analyse de sensibilité et l’assimilation de données. On étudie tout d’abord la modélisation rhéologique de ces fluides à travers les deux paramètres principaux de la loi de comportement : la consistance du fluide et l’exposant rhéologique. Des analyses de sensibilité sur ces paramètres définis localement, permettent de quantifier leurs poids relatifs au sein du modèle d’écoulement, en termes de vitesses de surface. L’identification de ces grandeurs est également réalisée. L’ensemble des résultats est résumé comme une méthodologie vers une “rhéométrie virtuelle” pouvant représenter une aide solide à la mesure rhéologique.Le glissement basal, paramètre majeur dans la dynamique de la glace, est investigué selon la même approche. Les analyses de sensibilité mettent en avant une capacité à voir à travers le caractère “filtré” et non-local de la transmission de la variabilité basale vers la surface, ouvrant des perspectives vers l’utilisation des sensibilités pour la définition de lieux d’intérêt pour l’observation et la mesure. Ce glissement basal, modélisation empirique d’un processus complexe et multiéchelle, est ensuite…
Advisors/Committee Members: Monnier, Jérôme (thesis director).
Subjects/Keywords: Viscoplasticité; Éléments finis; Analyse de sensibilité variationnelle; Assimilation de données; Glaciologie; Lagrangien augmenté; Différentiation automatique; Viscoplasticity; Finite elements; Variational sensitivity analysis; Data assimilation; Glaciology; Augmented Lagrangian; Automatic differentiation; 532
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APA (6th Edition):
Martin, N. (2013). Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology. (Doctoral Dissertation). Toulouse, INSA. Retrieved from http://www.theses.fr/2013ISAT0021
Chicago Manual of Style (16th Edition):
Martin, Nathan. “Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology.” 2013. Doctoral Dissertation, Toulouse, INSA. Accessed January 28, 2020.
http://www.theses.fr/2013ISAT0021.
MLA Handbook (7th Edition):
Martin, Nathan. “Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology.” 2013. Web. 28 Jan 2020.
Vancouver:
Martin N. Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology. [Internet] [Doctoral dissertation]. Toulouse, INSA; 2013. [cited 2020 Jan 28].
Available from: http://www.theses.fr/2013ISAT0021.
Council of Science Editors:
Martin N. Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology. [Doctoral Dissertation]. Toulouse, INSA; 2013. Available from: http://www.theses.fr/2013ISAT0021
18.
Hentz, Gauthier.
Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design.
Degree: Docteur es, Robotique, 2017, Université de Strasbourg
URL: http://www.theses.fr/2017STRAD021
► Dans le contexte médico-chirurgical, la robotique peut être d’un grand intérêt pour des procédures plus sûres et plus précises. Les contraintes d’encombrement sont cependant très…
(more)
▼ Dans le contexte médico-chirurgical, la robotique peut être d’un grand intérêt pour des procédures plus sûres et plus précises. Les contraintes d’encombrement sont cependant très fortes et des mobilités complexes peuvent être nécessaires. A ce jour, la conception de mécanismes non conventionnels dédiés est alors difficile à réaliser faute d’outils génériques permettant une évaluation rapide de leurs performances. Cette thèse associe la continuation de haut-degré et la différentiation automatique pour répondre à cette problématique en introduisant une méthode de modélisation et un formalisme génériques pour la conception de mécanismes. Nos contributions concernent en particulier le développement d’outils numériques pour l’évaluation de l’espace de travail, et de la localisation et la nature des singularités d’un mécanisme, et une analyse de sensibilité de haut-degré. Ceux-ci sont évalués sur des mécanismes de référence.
In the medical and surgical background, robotics can be of great interest for safer and more accurate procedures. Size constraints are however strong and complex movements may be necessary. To date, the design of dedicated non-conventional mechanisms is then a difficult task because of a lack of generic tools allowing a fast evaluation of their performances. This thesis combines higher-order continuation and automatic differentiation to adress this issue through the introduction of a generic modelling method and a generic formalism for mechanism design. Our contributions especially concern the development of numerical tools for the evaluation of the workspace, of the singularity localization and nature, and for a higher-order sensitivity analysis. These tools are evaluated on reference mechanisms.
Advisors/Committee Members: Charpentier, Isabelle (thesis director), Renaud, Pierre (thesis director).
Subjects/Keywords: Conception de mécanismes; Espace de travail; Analyse de singularité; Continuation de haut-degré; Différentiation automatique; Sensibilité; Mechanism design; Workspace; Singularity analysis; Higher-order continuation; Automatic differentiation; Sensitivity; 629.89
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APA (6th Edition):
Hentz, G. (2017). Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2017STRAD021
Chicago Manual of Style (16th Edition):
Hentz, Gauthier. “Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design.” 2017. Doctoral Dissertation, Université de Strasbourg. Accessed January 28, 2020.
http://www.theses.fr/2017STRAD021.
MLA Handbook (7th Edition):
Hentz, Gauthier. “Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design.” 2017. Web. 28 Jan 2020.
Vancouver:
Hentz G. Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2017. [cited 2020 Jan 28].
Available from: http://www.theses.fr/2017STRAD021.
Council of Science Editors:
Hentz G. Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design. [Doctoral Dissertation]. Université de Strasbourg; 2017. Available from: http://www.theses.fr/2017STRAD021
19.
LI, XIAO.
INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION.
Degree: MSc, 2017, McMaster University
URL: http://hdl.handle.net/11375/22521
► We propose two efficient automatic differentiation (AD) schemes to compute incrementally Taylor series and System Jacobian for solving differential-algebraic equations (DAEs) by Taylor series. Our…
(more)
▼ We propose two efficient automatic differentiation (AD) schemes to compute incrementally Taylor series and System Jacobian for solving differential-algebraic equations (DAEs) by Taylor series. Our schemes are based on topological ordering of a DAE's computational graph and then partitioning the topologically sorted nodes using structural information obtained from the DAE. Solving a DAE by Taylor series is carried out in stages. From one stage to another, partitions of the computational graph are incrementally activated so that we can reuse Taylor coefficients and gradients computed in previous stages. As a result, the computational complexity of evaluating a System Jacobian is independent of the number of stages.
We also develop a common subexpression elimination (CSE) method to build a compact computational graph through operator overloading. The CSE method is of linear time complexity, which makes it suitable as a preprocessing step for general operator overloaded computing. By applying CSE, all successive overloaded computation can save time and memory.
Furthermore, the computational graph of a DAE reveals its internal sparsity structure. Based on it, we devise an algorithm to propagate gradients in the forward mode of AD using compressed vectors. This algorithm can save both time and memory when computing the System Jacobian for sparse DAEs. We have integrated our approaches into the \daets solver. Computational results show multiple-fold speedups against two popular AD tools, \FAD~and ADOL-C, when solving various sparse and dense DAEs.
Thesis
Master of Science (MSc)
Advisors/Committee Members: Nedialkov, Nedialko, Computational Engineering and Science.
Subjects/Keywords: Automatic Differentiation; Differential-Algebraic Equations; Common Subexpression Elimination; Taylor Series
…hand side) via automatic differentiation (AD) to form the
underlying linear… …efficient evaluations of J and TCs in b
using automatic differentiation.
10
CHAPTER 2… …common subexpressions
during automatic differentiation. For all the examples in Chapter 4 and… …subexpressions by hand, if the differentiation is automated (which should be the case in practical… …step before computing. All successive
overloaded computing including automatic…
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APA (6th Edition):
LI, X. (2017). INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/22521
Chicago Manual of Style (16th Edition):
LI, XIAO. “INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION.” 2017. Masters Thesis, McMaster University. Accessed January 28, 2020.
http://hdl.handle.net/11375/22521.
MLA Handbook (7th Edition):
LI, XIAO. “INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION.” 2017. Web. 28 Jan 2020.
Vancouver:
LI X. INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION. [Internet] [Masters thesis]. McMaster University; 2017. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/11375/22521.
Council of Science Editors:
LI X. INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION. [Masters Thesis]. McMaster University; 2017. Available from: http://hdl.handle.net/11375/22521
Purdue University
20.
Barrett, Daniel P.
Learning in vision and robotics.
Degree: PhD, Electrical and Computer Engineering, 2016, Purdue University
URL: https://docs.lib.purdue.edu/open_access_dissertations/620
► I present my work on learning from video and robotic input. This is an important problem, with numerous potential applications. The use of machine…
(more)
▼ I present my work on learning from video and robotic input. This is an important problem, with numerous potential applications. The use of machine learning makes it possible to obtain models which can handle noise and variation without explicitly programming them. It also raises the possibility of robots which can interact more seamlessly with humans rather than only exhibiting hard-coded behaviors. I will present my work in two areas: video action recognition, and robot navigation. First, I present a video action recognition method which represents actions in video by sequences of retinotopic appearance and motion detectors, learns such models automatically from training data, and allow actions in new video to be recognized and localized completely automatically. Second, I present a new method which allows a mobile robot to learn word meanings from a combination of robot sensor measurements and sentential descriptions corresponding to a set of robotically driven paths. These word meanings support
automatic driving from sentential input, and generation of sentential description of new paths. Finally, I also present work on a new action recognition dataset, and comparisons of the performance of recent methods on this dataset and others.
Advisors/Committee Members: Jeffrey M. Siskind, Jeffrey M. Siskind, Robert L. Givan, Thomas M. Talavage, T. N. Vijaykumar.
Subjects/Keywords: Applied sciences; Automatic differentiation; Computer vision; Robot language comprehension; Robotic language learning; Video action localization; Video action recognition; Artificial Intelligence and Robotics; Computer Sciences; Robotics
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APA (6th Edition):
Barrett, D. P. (2016). Learning in vision and robotics. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/620
Chicago Manual of Style (16th Edition):
Barrett, Daniel P. “Learning in vision and robotics.” 2016. Doctoral Dissertation, Purdue University. Accessed January 28, 2020.
https://docs.lib.purdue.edu/open_access_dissertations/620.
MLA Handbook (7th Edition):
Barrett, Daniel P. “Learning in vision and robotics.” 2016. Web. 28 Jan 2020.
Vancouver:
Barrett DP. Learning in vision and robotics. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2020 Jan 28].
Available from: https://docs.lib.purdue.edu/open_access_dissertations/620.
Council of Science Editors:
Barrett DP. Learning in vision and robotics. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/620
Georgia Tech
21.
Takemiya, Tetsushi.
Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization.
Degree: PhD, Aerospace Engineering, 2008, Georgia Tech
URL: http://hdl.handle.net/1853/26515
► In modern aerospace engineering, the physics-based computational design method is becoming more important. However, high-fidelity models require longer computational time, so the advantage of efficiency…
(more)
▼ In modern aerospace engineering, the physics-based computational design method is becoming more important. However, high-fidelity models require longer computational time, so the advantage of efficiency is partially lost. This problem has been overcome with the development of the approximation management framework (AMF).
In the AMF, objective and constraint functions of a low-fidelity model are scaled at a design point so that the scaled functions, referred to as gsurrogate functions, h match those of a high-fidelity model. Since scaling functions and the low-fidelity model constitutes surrogate functions, evaluating the surrogate functions is faster than evaluating the high-fidelity model. Therefore, in the optimization process of the AMF, the surrogate functions are used to obtain a new design point.
However, the author found that 1) the AMF is very vulnerable when the computational analysis models have numerical noise, and that 2) the AMF terminates optimization prematurely when the optimization problems have constraints.
In order to solve the first problem,
automatic differentiation (AD) technique is applied. If derivatives are computed with the generated derivative code, they are analytical, and the computational time is independent of the number of design variables. However, if analysis models implement iterative computations such as computational fluid dynamics (CFD), computing derivatives through the AD requires a massive memory size. The author solved this deficiency by modifying the AD approach and developing a more efficient implementation with CFD.
In order to solve the second problem, the governing equation of the trust region ratio is modified so that it can accept the violation of constraints within some tolerance. By accepting violations of constraints during the optimization process, the AMF can continue optimization without terminating immaturely and eventually find the true optimum design point.
With these modifications, the AMF is referred to as gRobust AMF, h and it is applied to airfoil and wing designs using Euler CFD software. The proposed AD method computes derivatives more accurately and faster than the finite
differentiation method, and the Robust AMF successfully optimizes shapes of the airfoil and the wing in a much shorter time than the sequential quadratic programming with only high-fidelity models.
Advisors/Committee Members: Mavris, Dimitri (Committee Chair), Alley, Nicholas (Committee Member), Lakshmi, Sankar (Committee Member), Sriram, Rallabhandi (Committee Member), Stephen, Ruffin (Committee Member).
Subjects/Keywords: Optimization; Automatic differentiation; CFD; Aerodynamics; Design; Aerospace engineering; Computational fluid dynamics; Quadratic programming
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APA (6th Edition):
Takemiya, T. (2008). Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/26515
Chicago Manual of Style (16th Edition):
Takemiya, Tetsushi. “Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization.” 2008. Doctoral Dissertation, Georgia Tech. Accessed January 28, 2020.
http://hdl.handle.net/1853/26515.
MLA Handbook (7th Edition):
Takemiya, Tetsushi. “Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization.” 2008. Web. 28 Jan 2020.
Vancouver:
Takemiya T. Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization. [Internet] [Doctoral dissertation]. Georgia Tech; 2008. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/1853/26515.
Council of Science Editors:
Takemiya T. Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization. [Doctoral Dissertation]. Georgia Tech; 2008. Available from: http://hdl.handle.net/1853/26515
22.
Auliac, Sylvain.
développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++.
Degree: Docteur es, Mathématiques, 2014, Université Pierre et Marie Curie – Paris VI
URL: http://www.theses.fr/2014PA066035
► Cette thèse est consacrée au développement d'outils pour FreeFem++ destinés à faciliter la résolution des problèmes d'optimisation. Ce travail se compose de deux parties principales.…
(more)
▼ Cette thèse est consacrée au développement d'outils pour FreeFem++ destinés à faciliter la résolution des problèmes d'optimisation. Ce travail se compose de deux parties principales. La première consiste en la programmation, la validation et l'exploitation d'interfaces permettant l¿utilisation de routines d'optimisation directement dans le logiciel. La seconde comprend le développement de solutions pour le calcul automatisé des dérivées, toujours au sein de FreeFem++, en exploitant les paradigmes de la différentiation automatique. FreeFem++ est un environnement de développement intégré dédié à la résolution numérique d¿équations aux dérivées partielles en dimension 2 et 3. Son langage ergonomique permet à l'utilisateur d'exploiter aisément ses nombreux outils de création de maillages, de résolution de systèmes linéaires, ainsi que ses bibliothèques d'éléments finis, etc... Nous introduisons les nouvelles routines d'optimisation désormais accessibles depuis la bibliothèque de modules du logiciel. En particulier, le logiciel libre d'optimisation sous contraintes IPOPT, qui implémente une méthode de points intérieurs très robuste pour l¿optimisation en grande dimension. Nous appliquons avec succès ces algorithmes à une série de problèmes concrets parmi lesquels la résolution numérique de problèmes de sur- faces minimales, la simulation de condensats de Bose-Einstein, ou encore un problème de positionnement inverse en mécanique des fluides. Une version prototypique de FreeFem++ contenant les outils de différentiation automatique est présentée, après avoir exposé les principes fondamentaux de cette méthode de calcul de dérivées pour le calcul scientifique.
The goal of this Ph.D. thesis was the development of tools for the FreeFem++ software in order to make optimization problems easier to deal with. This has been accomplished following two main directions. Firstly, a set of optimization softwares is interfaced and validated before making use of them. Then, we analyse the field of automatic differentiation as a potential mean of simplification for the users. FreeFem++ is an integrated development environment dedicated to numerically solving partial differential equations. Its high level language allows the user for a comfortable experience while using its mesh generation capabilities, linear system solvers, as well as finite elements capabilities. We describe the newly available optimization features, with a certain emphasis on the open source software IPOPT, which implements a state of the art interior points method for large scale optimization. These optimization tools are then used in a set of quite successful applications, among which minimal surfaces, Bose-Einstein condensate simulation, and an inverse positioning problem in the context of computational fluid dynamics. Finally, after an introduction to the techniques of algorithmic differentiation, we also present an unstable prototype version of FreeFem++ including automatic differentiation features.
Advisors/Committee Members: Hecht, Frédéric (thesis director).
Subjects/Keywords: Calcul scientifique; Développement de logiciel; Différentiation automatique; Méthode des éléments finis; Équations aux dérivées partielles; Optimisation; Automatic differentiation; Finite elements method; 510
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APA (6th Edition):
Auliac, S. (2014). développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++. (Doctoral Dissertation). Université Pierre et Marie Curie – Paris VI. Retrieved from http://www.theses.fr/2014PA066035
Chicago Manual of Style (16th Edition):
Auliac, Sylvain. “développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++.” 2014. Doctoral Dissertation, Université Pierre et Marie Curie – Paris VI. Accessed January 28, 2020.
http://www.theses.fr/2014PA066035.
MLA Handbook (7th Edition):
Auliac, Sylvain. “développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++.” 2014. Web. 28 Jan 2020.
Vancouver:
Auliac S. développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++. [Internet] [Doctoral dissertation]. Université Pierre et Marie Curie – Paris VI; 2014. [cited 2020 Jan 28].
Available from: http://www.theses.fr/2014PA066035.
Council of Science Editors:
Auliac S. développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++. [Doctoral Dissertation]. Université Pierre et Marie Curie – Paris VI; 2014. Available from: http://www.theses.fr/2014PA066035
Humboldt University of Berlin
23.
Diels-Grabsch, Volker.
Parallel reversal schedules using more checkpoints than processors.
Degree: 2015, Humboldt University of Berlin
URL: http://edoc.hu-berlin.de/docviews/abstract.php?id=42493
;
http://edoc.hu-berlin.de/master/diels-grabsch-volker-2015-09-24/PDF/diels-grabsch.pdf
;
http://www.nbn-resolving.de/urn:nbn:de:kobv:11-100236764
► Parallele Umkehr-Ablaufpläne (Parallel reversal schedules) beschreiben, wie die Zustände eines evolutionären Systems, etwa einer atmosphärischen oder ozeanographischen Simulation, in umgekehrter Reihenfolge berechnet werden können, ohne…
(more)
▼ Parallele Umkehr-Ablaufpläne (Parallel reversal schedules) beschreiben, wie die Zustände eines evolutionären Systems, etwa einer atmosphärischen oder ozeanographischen Simulation, in umgekehrter Reihenfolge berechnet werden können, ohne dass alle Zustände im Speicher gehalten werden müssen. Auf einem Mehrprozessorsystem ist das ohne Anstieg der benötigten Rechenzeit möglich, indem Zwischenergebnisse zwar mehrfach berechnet werden, aber gleichzeitig auf mehreren Prozessoren. Diese Ablaufpläne werden nicht nur verwendet, um Simulationen rückwärts abzuspielen, sondern auch in der algorithmischen Differenzierung, die wiederum in der nichtlinearen Optimierung sowie beim Lösen von partiellen Differentialgleichungen eingesetzt wird. Die bisherige Forschung ermittelte optimale Pläne für den Fall, dass folgende zentrale Annahme erfüllt ist: Können k Zustände gleichzeitig im Speicher gehalten werden, so sind stets etwa k/2 Prozessoren verfügbar, die die Berechnung von k/2 Zuständen fortsetzen. Die übrigen k/2 Zustände werden in reinen Speicherpunkten (Checkpoints) vorgehalten. In dieser Diplomarbeit wird die zentrale Annahme gelockert und so die Forschung fortgesetzt. Es ist nun möglich, dass deutlich weniger als k/2 Prozessoren verfügbar sind, oder gleichbedeutend, dass viel mehr Speicherpunkte genutzt werden können. Für diese neue Aufgabenstellung wird eine symbolische Herangehensweise an parallele Umkehr-Ablaufpläne vorgestellt. Es wird eine umfassende Algebra entwickelt, die einen direkten Zugang zu den Profilen der Pläne bietet und so deren Analyse erleichtert. Diese Algebra ist sehr generisch und könnte weitere Anwendungen haben. Es werden neue Pläne entwickelt, die in Situationen anwendbar sind, in denen die bisher bekannten Pläne ungeeignet waren. In einigen Fällen sind sie optimal, für alle übrigen Fälle werden suboptimale Pläne vorgestellt, die ebenfalls eine deutliche Verbesserung zu den bisherigen Plänen darstellen.
Parallel reversal schedules describe how to calculate the states of an evolutionary system, such as atmospheric and oceanographic simulations, in reverse order without having to keep all states in memory. This is possible without any increase in computation time, by recalculating intermediate results using multiple processors on a parallel computer system. These schedules are not only applied physical simulations that need to run in reverse, but also in algorithmic differentiation, which in turn is used, among others, in nonlinear optimization and to solve partial differential equations. Earlier research led to optimal schedules under the central assumption that if k states can be kept in memory, there are enough processors to run computations on roughly half of them in parallel, while the other half can only be used for holding checkpoints. This diploma thesis is an attempt to continue the research by relaxing the central assumption, such that memory for a large number of plain checkpoints can be used with a comparatively small number of processors. To cope with this challenge, a…
Advisors/Committee Members: Griewank, Andreas, Walther, Andrea.
Subjects/Keywords: Mathematik; Mathematik; mathematics; Simulation; simulation; automatic differentiation; scheduling; Diplomarbeit; diploma thesis; automatisches Differenzieren; algorithmisches Differenzieren; Scheduling; Rückwärts-Ablaufpläne; Diskrete Optimierung; Parallelrechner; algorithmic differentiation; reversal schedules; discrete optimization; parallel computing; ddc:510
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APA (6th Edition):
Diels-Grabsch, V. (2015). Parallel reversal schedules using more checkpoints than processors. (Masters Thesis). Humboldt University of Berlin. Retrieved from http://edoc.hu-berlin.de/docviews/abstract.php?id=42493 ; http://edoc.hu-berlin.de/master/diels-grabsch-volker-2015-09-24/PDF/diels-grabsch.pdf ; http://www.nbn-resolving.de/urn:nbn:de:kobv:11-100236764
Chicago Manual of Style (16th Edition):
Diels-Grabsch, Volker. “Parallel reversal schedules using more checkpoints than processors.” 2015. Masters Thesis, Humboldt University of Berlin. Accessed January 28, 2020.
http://edoc.hu-berlin.de/docviews/abstract.php?id=42493 ; http://edoc.hu-berlin.de/master/diels-grabsch-volker-2015-09-24/PDF/diels-grabsch.pdf ; http://www.nbn-resolving.de/urn:nbn:de:kobv:11-100236764.
MLA Handbook (7th Edition):
Diels-Grabsch, Volker. “Parallel reversal schedules using more checkpoints than processors.” 2015. Web. 28 Jan 2020.
Vancouver:
Diels-Grabsch V. Parallel reversal schedules using more checkpoints than processors. [Internet] [Masters thesis]. Humboldt University of Berlin; 2015. [cited 2020 Jan 28].
Available from: http://edoc.hu-berlin.de/docviews/abstract.php?id=42493 ; http://edoc.hu-berlin.de/master/diels-grabsch-volker-2015-09-24/PDF/diels-grabsch.pdf ; http://www.nbn-resolving.de/urn:nbn:de:kobv:11-100236764.
Council of Science Editors:
Diels-Grabsch V. Parallel reversal schedules using more checkpoints than processors. [Masters Thesis]. Humboldt University of Berlin; 2015. Available from: http://edoc.hu-berlin.de/docviews/abstract.php?id=42493 ; http://edoc.hu-berlin.de/master/diels-grabsch-volker-2015-09-24/PDF/diels-grabsch.pdf ; http://www.nbn-resolving.de/urn:nbn:de:kobv:11-100236764
Cornell University
24.
Tien, Joseph.
Optimization for Bursting Neural Models
.
Degree: 2006, Cornell University
URL: http://hdl.handle.net/1813/3504
► This thesis concerns parameter estimation for bursting neural models. Parameter estimation for differential equations is a difficult task due to complicated objective function landscapes and…
(more)
▼ This thesis concerns parameter estimation for bursting neural models. Parameter estimation for differential equations is a difficult task due to complicated objective function landscapes and numerical challenges. These difficulties are particularly salient in bursting models and other multiple time scale systems. Here we make use of the geometry underlying bursting by introducing defining equations for burst initiation and termination. Fitting the timing of these burst events simplifies objective function landscapes considerably. We combine this with automatic differentiation to accurately compute gradients for these burst events, and implement these features using standard unconstrained optimization algorithms. We use trajectories from a minimal spiking model and the Hindmarsh-Rose equations as test problems, and bursting respiratory neurons in the preBotzinger complex as an application. These geometrical ideas and numerical improvements significantly enhance algorithm performance. Excellent fits are obtained to the preBotzinger data both in control conditions and when the neuromodulator norepinephrine is added. The results suggest different possible neuromodulatory mechanisms, and help analyze the roles of different currents in shaping burst duration and period.
Subjects/Keywords: optimization;
bursting;
neural models;
parameter estimation;
preBotzinger;
Hodgkin-Huxley;
automatic differentiation;
algorithmic differentiation;
dynamical systems;
differential equations
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APA (6th Edition):
Tien, J. (2006). Optimization for Bursting Neural Models
. (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/3504
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Tien, Joseph. “Optimization for Bursting Neural Models
.” 2006. Thesis, Cornell University. Accessed January 28, 2020.
http://hdl.handle.net/1813/3504.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Tien, Joseph. “Optimization for Bursting Neural Models
.” 2006. Web. 28 Jan 2020.
Vancouver:
Tien J. Optimization for Bursting Neural Models
. [Internet] [Thesis]. Cornell University; 2006. [cited 2020 Jan 28].
Available from: http://hdl.handle.net/1813/3504.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Tien J. Optimization for Bursting Neural Models
. [Thesis]. Cornell University; 2006. Available from: http://hdl.handle.net/1813/3504
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Université de Grenoble
25.
Pham-Quang, Phuong.
Modélisation magnéto-mécanique d'un nano commutateur. Optimisation sous contraintes de fiabilité par dérivation automatique des programmes en Java : Magneto-mechanical modelling of nano switch. Reliability-based design optimization by automatic differentiation in Java.
Degree: Docteur es, Sciences et technologie industrielles, 2011, Université de Grenoble
URL: http://www.theses.fr/2011GRENT060
► Les nano commutateurs magnétiques sont en cours d'étude et ils sont envisageables dans plusieurs domaines d'application comme les interrupteurs d'alimentation, les convertisseurs DC/DC...etc. Partant du…
(more)
▼ Les nano commutateurs magnétiques sont en cours d'étude et ils sont envisageables dans plusieurs domaines d'application comme les interrupteurs d'alimentation, les convertisseurs DC/DC...etc. Partant du besoin de modélisation et d'optimisation avec fiabilité de ces dispositifs, ces travaux de thèse se décomposent en trois axes. Axe modélisation : développement d'un modèle semi analytique pour calculer la déformation avec l'analyse de contact mécanique. Ce modèle a été introduit pour le couplage magnéto-mécanique dans le logiciel de modélisation de MEMS magnétiques MacMMems. Axe dérivation automatique de code : développement de JAP (Java Jacobian Automatic Programming) qui est un outil générique de dérivation d'algorithmes. Il a été appliqué pour le nano commutateur et a été introduit dans les outils de dimensionnement développés au G2Elab pour l'analyse de sensibilité, pour l'optimisation exploitant le Jacobien et aussi pour orienter des systèmes d'équations algébro-différentiels. Axe optimisation : mise en œuvre du modèle et des outils développés pour faire l'étude de sensibilité et l'optimisation sous contraintes de fiabilité du nano commutateur magnétique.
Magnetic nano switches are being studied and they are envisaged in several application areas such as power switches, DC / DC converters …etc. Hence the need for modelling and optimization with reliability of these devices, this thesis work is divided into three areas. Modelling: development of a semi analytical model to calculate the deformation with the analysis of mechanical contact. This model was introduced in the “MacMMems” software dedicated to the modelling of magnetic MEMS. Automatic differentiation : development of JAP (Java Jacobian Automatic Programming) is a generic algorithms derivation program. It has been applied to the nano switch and was introduced in G2Elab design tools for sensitivity analysis, for optimizing and also to solve differential-algebraic systems. Optimization: development the model and tools to study the sensitivity and reliability-based design optimization for magnetic nano switch.
Advisors/Committee Members: Coulomb, Jean-Louis (thesis director), Delinchant, Benoit (thesis director).
Subjects/Keywords: Analyse de contact; Couplage magnéto-mécanique; Couplage magnéto-mécanique; Dérivation automatique de code; Analyse de sensibilité; Optimisation avec fiabilité; Contact analysis; Magneto-mechanical coupling; Nano magnetic switch; Automatic differentiation; Sensitivity analysis; Optimization reliable
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APA ·
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APA (6th Edition):
Pham-Quang, P. (2011). Modélisation magnéto-mécanique d'un nano commutateur. Optimisation sous contraintes de fiabilité par dérivation automatique des programmes en Java : Magneto-mechanical modelling of nano switch. Reliability-based design optimization by automatic differentiation in Java. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2011GRENT060
Chicago Manual of Style (16th Edition):
Pham-Quang, Phuong. “Modélisation magnéto-mécanique d'un nano commutateur. Optimisation sous contraintes de fiabilité par dérivation automatique des programmes en Java : Magneto-mechanical modelling of nano switch. Reliability-based design optimization by automatic differentiation in Java.” 2011. Doctoral Dissertation, Université de Grenoble. Accessed January 28, 2020.
http://www.theses.fr/2011GRENT060.
MLA Handbook (7th Edition):
Pham-Quang, Phuong. “Modélisation magnéto-mécanique d'un nano commutateur. Optimisation sous contraintes de fiabilité par dérivation automatique des programmes en Java : Magneto-mechanical modelling of nano switch. Reliability-based design optimization by automatic differentiation in Java.” 2011. Web. 28 Jan 2020.
Vancouver:
Pham-Quang P. Modélisation magnéto-mécanique d'un nano commutateur. Optimisation sous contraintes de fiabilité par dérivation automatique des programmes en Java : Magneto-mechanical modelling of nano switch. Reliability-based design optimization by automatic differentiation in Java. [Internet] [Doctoral dissertation]. Université de Grenoble; 2011. [cited 2020 Jan 28].
Available from: http://www.theses.fr/2011GRENT060.
Council of Science Editors:
Pham-Quang P. Modélisation magnéto-mécanique d'un nano commutateur. Optimisation sous contraintes de fiabilité par dérivation automatique des programmes en Java : Magneto-mechanical modelling of nano switch. Reliability-based design optimization by automatic differentiation in Java. [Doctoral Dissertation]. Université de Grenoble; 2011. Available from: http://www.theses.fr/2011GRENT060
26.
Herrmann, Julien.
Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel.
Degree: Docteur es, Informatique, 2015, Lyon, École normale supérieure
URL: http://www.theses.fr/2015ENSL1043
► Dans cette thèse, nous nous sommes penchés d’un point de vue à la foisthéorique et pratique sur la conception d’algorithmes et detechniques d’ordonnancement adaptées aux…
(more)
▼ Dans cette thèse, nous nous sommes penchés d’un point de vue à la foisthéorique et pratique sur la conception d’algorithmes et detechniques d’ordonnancement adaptées aux architectures complexes dessuperordinateurs modernes. Nous nous sommes en particulier intéressésà l’utilisation mémoire et la gestion des communications desalgorithmes pour le calcul haute performance (HPC). Nous avonsexploité l’hétérogénéité des superordinateurs modernes pour améliorerles performances du calcul matriciel. Nous avons étudié lapossibilité d’alterner intelligemment des étapes de factorisation LU(plus rapide) et des étapes de factorisation QR (plus stablenumériquement mais plus deux fois plus coûteuses) pour résoudre unsystème linéaire dense. Nous avons amélioré les performances desystèmes d’exécution dynamique à l’aide de pré-calculs statiquesprenants en compte l’ensemble du graphe de tâches de la factorisationCholesky ainsi que l’hétérogénéité de l’architecture. Nous noussommes intéressés à la complexité du problème d’ordonnancement degraphes de tâches utilisant de gros fichiers d’entrée et de sortiesur une architecture hétérogène avec deux types de ressources,utilisant chacune une mémoire spécifique. Nous avons conçu denombreuses heuristiques en temps polynomial pour la résolution deproblèmes généraux que l’on avait prouvés NP-complet aupréalable. Enfin, nous avons conçu des algorithmes optimaux pourordonnancer un graphe de différentiation automatique sur uneplateforme avec deux types de mémoire : une mémoire gratuite maislimitée et une mémoire coûteuse mais illimitée.
Throughout this thesis, we have designed memory-aware algorithms and scheduling techniques suitedfor modern memory architectures. We have shown special interest in improving the performance ofmatrix computations on multiple levels. At a high level, we have introduced new numerical algorithmsfor solving linear systems on large distributed platforms. Most of the time, these linear solvers rely onruntime systems to handle resources allocation and data management. We also focused on improving thedynamic schedulers embedded in these runtime systems by adding static information to their decisionprocess. We proposed new memory-aware dynamic heuristics to schedule workflows, that could beimplemented in such runtime systems.Altogether, we have dealt with multiple state-of-the-art factorization algorithms used to solve linearsystems, like the LU, QR and Cholesky factorizations. We targeted different platforms ranging frommulticore processors to distributed memory clusters, and worked with several reference runtime systemstailored for these architectures, such as P A RSEC and StarPU. On a theoretical side, we took specialcare of modelling convoluted hierarchical memory architectures. We have classified the problems thatare arising when dealing with these storage platforms. We have designed many efficient polynomial-timeheuristics on general problems that had been shown NP-complete beforehand.
Advisors/Committee Members: Robert, Yves (thesis director).
Subjects/Keywords: Ordonnancement multi-critère; Algorithmes numériques; Factorisation LU; Factorisation QR; Factorisation Cholesky; Calcul haute performance; Systèmes linéaires; Différentiation automatique; Scheduling; Numerical algorithms; LU factorization; QR factorization; Cholesky factorization; High performance computing; Linear systems; Automatic differentiation
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APA ·
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CSE |
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APA (6th Edition):
Herrmann, J. (2015). Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel. (Doctoral Dissertation). Lyon, École normale supérieure. Retrieved from http://www.theses.fr/2015ENSL1043
Chicago Manual of Style (16th Edition):
Herrmann, Julien. “Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel.” 2015. Doctoral Dissertation, Lyon, École normale supérieure. Accessed January 28, 2020.
http://www.theses.fr/2015ENSL1043.
MLA Handbook (7th Edition):
Herrmann, Julien. “Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel.” 2015. Web. 28 Jan 2020.
Vancouver:
Herrmann J. Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; 2015. [cited 2020 Jan 28].
Available from: http://www.theses.fr/2015ENSL1043.
Council of Science Editors:
Herrmann J. Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel. [Doctoral Dissertation]. Lyon, École normale supérieure; 2015. Available from: http://www.theses.fr/2015ENSL1043
27.
Yang, Jie.
Solving Partial Differential Equations by Taylor Meshless Method : La modélisation avancée et la simulation en utilisant la série de Taylor.
Degree: Docteur es, Mécanique et énergétique, 2018, Université de Lorraine; Université de Wuhan (Chine)
URL: http://www.theses.fr/2018LORR0032
► Le but de cette thèse est de développer une méthode numérique simple, robuste, efficace et précise pour résoudre des problèmes d'ingénierie de grande taille à…
(more)
▼ Le but de cette thèse est de développer une méthode numérique simple, robuste, efficace et précise pour résoudre des problèmes d'ingénierie de grande taille à partir de la méthode Taylor Meshless (TMM) et fournir de nouvelles idées principales de TMM est d'utiliser comme fonctions de forme des polynômes d'ordre élevé qui sont des solutions approchées de l'EDP. Ainsi la discrétisation ne concerne que la frontière. Les coefficients de ces fonctions de forme sont obtenus en discrétisant les conditions aux limites par des procédures de collocation associées à la méthode des moindres carrés. TMM est alors une véritable méthode sans maillage sans processus d'intégration, les conditions aux limites étant obtenues par collocation. Les principales contributions de cette thèse sont les suivantes: 1) Basé sur TMM, un algorithme général et efficace a été développé pour résoudre des EDP elliptiques tridimensionnelles; 2) Trois techniques de couplage pour des résolutions par morceaux ont été discutées dans des cas de problèmes à grande échelle: la méthode de collocation par les moindres carrés et deux méthodes de couplage basées sur les multiplicateurs de Lagrange; 3) Une méthode numérique générale pour résoudre les EDP non-linéaires a été proposée en combinant la méthode de Newton, la TMM et la technique de différentiation automatique. 4) Pour résoudre des problèmes avec un bord non régulier, des solutions singulières satisfaisant l'équation de contrôle sont introduites comme des fonctions de forme complémentaires, ce qui fournit une base théorique pour la résolution de problèmes singuliers
Based on Taylor Meshless Method (TMM), the aim of this thesis is to develop a simple, robust, efficient and accurate numerical method which is capable of solving large scale engineering problems and to provide a new idea for the follow-up study on meshless methods. To this end, the influence of the key factors in TMM has been studied by solving three-dimensional and non-linear Partial Differential Equations (PDEs). The main idea of TMM is to use high order polynomials as shape functions which are approximated solutions of the PDE and the discretization concerns only the boundary. To solve the unknown coefficients, boundary conditions are accounted by collocation procedures associated with least-square method. TMM that needs only boundary collocation without integration process, is a true meshless method. The main contributions of this thesis are as following: 1) Based on TMM, a general and efficient algorithm has been developed for solving three-dimensional PDEs; 2) Three coupling techniques in piecewise resolutions have been discussed and tested in cases of large-scale problems, including least-square collocation method and two coupling methods based on Lagrange multipliers; 3) A general numerical method for solving non-linear PDEs has been proposed by combining Newton Method, TMM and Automatic Differentiation technique; 4) To apply TMM for solving problems with singularities, the singular solutions satisfying the control equation are…
Advisors/Committee Members: Potier-Ferry, Michel (thesis director), Hu, Heng (thesis director).
Subjects/Keywords: Série de Taylor; Méthode sans maillage; Résolution par morceaux; Différenciation automatique; Fonctions de forme singulières; Équations aux dérivées partielles; Taylor series; Meshless method; Coupling techniques in piecewise resolution; Automatic differentiation; Singular shape function; Partial differential equation; 530.1
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APA ·
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APA (6th Edition):
Yang, J. (2018). Solving Partial Differential Equations by Taylor Meshless Method : La modélisation avancée et la simulation en utilisant la série de Taylor. (Doctoral Dissertation). Université de Lorraine; Université de Wuhan (Chine). Retrieved from http://www.theses.fr/2018LORR0032
Chicago Manual of Style (16th Edition):
Yang, Jie. “Solving Partial Differential Equations by Taylor Meshless Method : La modélisation avancée et la simulation en utilisant la série de Taylor.” 2018. Doctoral Dissertation, Université de Lorraine; Université de Wuhan (Chine). Accessed January 28, 2020.
http://www.theses.fr/2018LORR0032.
MLA Handbook (7th Edition):
Yang, Jie. “Solving Partial Differential Equations by Taylor Meshless Method : La modélisation avancée et la simulation en utilisant la série de Taylor.” 2018. Web. 28 Jan 2020.
Vancouver:
Yang J. Solving Partial Differential Equations by Taylor Meshless Method : La modélisation avancée et la simulation en utilisant la série de Taylor. [Internet] [Doctoral dissertation]. Université de Lorraine; Université de Wuhan (Chine); 2018. [cited 2020 Jan 28].
Available from: http://www.theses.fr/2018LORR0032.
Council of Science Editors:
Yang J. Solving Partial Differential Equations by Taylor Meshless Method : La modélisation avancée et la simulation en utilisant la série de Taylor. [Doctoral Dissertation]. Université de Lorraine; Université de Wuhan (Chine); 2018. Available from: http://www.theses.fr/2018LORR0032
Université de Lorraine
28.
Kpeky, Fessal.
Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures.
Degree: Docteur es, Sciences des matériaux, 2016, Université de Lorraine
URL: http://www.theses.fr/2016LORR0008
► Cette thèse s’intéresse au développement d’éléments finis solide–coques dédiés à la modélisation de structures multicouches sollicitées en vibrations. En effet, la plupart des modèles multicouches…
(more)
▼ Cette thèse s’intéresse au développement d’éléments finis solide–coques dédiés à la modélisation de structures multicouches sollicitées en vibrations. En effet, la plupart des modèles multicouches dans la littérature présentent des limitations dans certaines configurations géométriques et matérielles. Face à ce constat et dans un souci de proposer un outil moins coûteux en temps de calcul, nous avons proposé une approche basée sur le concept solide–coques. Il s’agit d’éléments finis tridimensionnels dont le comportement a été amélioré par l’Assumed Strain Method. Dans un premier temps, nous avons formulé le problème de vibrations de structures sandwichs à cœur viscoélastique. La dépendance en fréquence a ainsi été prise en compte en utilisant une loi constitutive complexe. Pour résoudre le problème discrétisé, la Méthode Asymptotique Numérique, couplée à l’homotopie, et utilisant l’approche DIAMANT, a été adoptée pour les excellents résultats qu’elle offre par rapport aux autres méthodes. Des tests ont permis de valider les modèles proposés et de montrer l’avantage par rapport aux éléments ayant la même cinématique. Poursuivant nos travaux, et dans un souci d’augmenter l’amortissement, nous nous sommes orientés vers un contrôle actif des vibrations. Pour ce faire, deux éléments finis piézoélectriques ont été formulés. Il s’agit des éléments SHB8PSE et SHB20E qui sont des extensions des éléments finis SHB8PS et SHB20, respectivement. Le couplage électromécanique a consisté en l’ajout d’un degré de liberté à chacun des nœuds des dits éléments. Quelques exemples en statique et en vibrations menés sur des structures multicouches allant de simples poutres aux structures présentant des non-linéarités géométriques ont permis de valider les éléments solide–coques proposés. Pour finir, une synthèse des acquis des chapitres 2 et 3 a permis de proposer une modélisation de structures multicouches comprenant des couches élastiques, viscoélastiques et piézoélectriques. À l’amortissement passif provenant du pouvoir amortissant des matériaux viscoélastiques, on ajoute un contrôle actif qui découle du courant électrique généré au cours de la déformation des couches piézoélectriques. Ainsi, un filtre a été installé entre les capteurs et actionneurs. Ce filtre permet d’amplifier ou d’atténuer le potentiel électrique généré dans le but de réduire les amplitudes de vibrations. Pour résoudre le problème résultant nous avons étendu le solveur utilisé au chapitre 2. Pour valider les modèles proposés, des tests de contrôle actif–passif ont été menés sur des structures plaques multicouches. Enfin, quelques lois de contrôle découlant de filtres ont permis de montrer comment cette procédure permet de réduire ou même d’éviter l’amplification des vibrations
This thesis deals with the development of solid–shell finite elements for vibration modeling of multilayer structures. Indeed, most of multilayer models in the literature show some limitations in certain geometric and material configurations. Considering these restrictions and in order to…
Advisors/Committee Members: Abed-Meraim, Farid (thesis director), Daya, El Mostafa (thesis director).
Subjects/Keywords: Éléments finis solide–coques; Méthode « Assumed Strain »; Structures multicouches; Vibrations; Viscoélasticité; Piézoélectricité; Amortissement passif; Contrôle actif; Différentiation Automatique; Méthode Asymptotique Numérique; Solid–shell finite elements; Assumed Strain Method; Multilayer structures; Vibrations; Viscoelasticity; Piezoelectricity; Passive damping; Active control; Automatic Differentiation; Asymptotic Numerical Method; 620.3; 620.112 48
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Kpeky, F. (2016). Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures. (Doctoral Dissertation). Université de Lorraine. Retrieved from http://www.theses.fr/2016LORR0008
Chicago Manual of Style (16th Edition):
Kpeky, Fessal. “Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures.” 2016. Doctoral Dissertation, Université de Lorraine. Accessed January 28, 2020.
http://www.theses.fr/2016LORR0008.
MLA Handbook (7th Edition):
Kpeky, Fessal. “Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures.” 2016. Web. 28 Jan 2020.
Vancouver:
Kpeky F. Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures. [Internet] [Doctoral dissertation]. Université de Lorraine; 2016. [cited 2020 Jan 28].
Available from: http://www.theses.fr/2016LORR0008.
Council of Science Editors:
Kpeky F. Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures. [Doctoral Dissertation]. Université de Lorraine; 2016. Available from: http://www.theses.fr/2016LORR0008
University of Oxford
29.
Ghate, Devendra.
Inexpensive uncertainty analysis for CFD applications.
Degree: PhD, 2014, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:6be44a1d-6e2f-4bf9-b1e5-1468f92e21e3
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.640090
► The work presented in this thesis aims to provide various tools to be used during design process to make maximum use of the increasing availability…
(more)
▼ The work presented in this thesis aims to provide various tools to be used during design process to make maximum use of the increasing availability of accurate engine blade measurement data for high fidelity fluid mechanic simulations at a reasonable computational expense. A new method for uncertainty propagation for geometric error has been proposed for fluid mechanics codes using adjoint error correction. Inexpensive Monte Carlo (IMC) method targets small uncertainties and provides complete probability distribution for the objective function at a significantly reduced computational cost. A brief literature survey of the existing methods is followed by the formulation of IMC. An example algebraic model is used to demonstrate the IMC method. The IMC method is extended to fluid mechanic applications using Principal Component Analysis (PCA) for reduced order modelling. Implementation details for the IMC method are discussed using an example airfoil code. Finally, the IMC method has been implemented and validated for an industrial fluid mechanic code HYDRA. A consistent methodology has been developed for the automatic generation of the linear and adjoint codes by selective use of automatic differentiation (AD) technique. The method has the advantage of keeping the linear and the adjoint codes in-sync with the changes in the underlying nonlinear fluid mechanic solver. The use of various consistency checks have been demonstrated to ease the development and maintenance process of the linear and the adjoint codes. The use of AD has been extended for the calculation of the complete Hessian using forward-on-forward approach. The complete mathematical formulation for Hessian calculation using the linear and the adjoint solutions has been outlined for fluid mechanic solvers. An efficient implementation for the Hessian calculation is demonstrated using the airfoil code. A new application of the Independent Component Analysis (ICA) is proposed for manufacturing uncertainty source identification. The mathematical formulation is outlined followed by an example application of ICA for artificially generated uncertainty for the NACA0012 airfoil.
Subjects/Keywords: 519.2; Fluid mechanics (mathematics); Numerical analysis; Partial differential equations; Aeronautical research; Aero engines; Mathematical modeling (engineering); Turbomachinery hypersonics and aerodynamics; Uncertainty analysis; Monte Carlo; Adjoint error correction; manufacturing uncertainty; Automatic Differentiation; Independent Component Analysis
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APA (6th Edition):
Ghate, D. (2014). Inexpensive uncertainty analysis for CFD applications. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:6be44a1d-6e2f-4bf9-b1e5-1468f92e21e3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.640090
Chicago Manual of Style (16th Edition):
Ghate, Devendra. “Inexpensive uncertainty analysis for CFD applications.” 2014. Doctoral Dissertation, University of Oxford. Accessed January 28, 2020.
http://ora.ox.ac.uk/objects/uuid:6be44a1d-6e2f-4bf9-b1e5-1468f92e21e3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.640090.
MLA Handbook (7th Edition):
Ghate, Devendra. “Inexpensive uncertainty analysis for CFD applications.” 2014. Web. 28 Jan 2020.
Vancouver:
Ghate D. Inexpensive uncertainty analysis for CFD applications. [Internet] [Doctoral dissertation]. University of Oxford; 2014. [cited 2020 Jan 28].
Available from: http://ora.ox.ac.uk/objects/uuid:6be44a1d-6e2f-4bf9-b1e5-1468f92e21e3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.640090.
Council of Science Editors:
Ghate D. Inexpensive uncertainty analysis for CFD applications. [Doctoral Dissertation]. University of Oxford; 2014. Available from: http://ora.ox.ac.uk/objects/uuid:6be44a1d-6e2f-4bf9-b1e5-1468f92e21e3 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.640090
University of South Florida
30.
Patel, Keyurkumar S.
Automatic generation of global phase equilibrium diagram from equation of state.
Degree: 2007, University of South Florida
URL: https://scholarcommons.usf.edu/etd/2318
► A computational tool that uses an automated and reliable procedure for systematic generation of global phase equilibrium diagram (GPED) is developed for binary system using…
(more)
▼ A computational tool that uses an automated and reliable procedure for systematic generation of global phase equilibrium diagram (GPED) is developed for binary system using equation of state and its extension to the ternary system is discussed. The proposed algorithm can handle solid phase and also can predict all major six types of phase diagrams. The procedure enables automatic generation of GPED which incorporates calculations of all important landmarks such as critical endpoints, quadruple point (if any), critical line, liquid-liquid-vapor line (if any), solid-liquid-liquid line (if any) and solid-liquid-vapor line. The method is also capable of locating all azeotropic phenomena such as azeotropic endpoint, critical azeotrope, pure azeotropic point and azeotropic lines. Although, we demonstrated the methodology for cubic equation of state, the proposed strategy is completely general that doesn't require any knowledge about the type of phase diagram and can be applied to any pressure explicit equation of state model. Newton homotopy based global method has been applied for phase stability test and critical point calculations to ensure reliability. Having computed the binary phase diagrams, the methodology to generate global phase diagrams for ternary system is discussed that can locate all important thermodynamic landmarks such as tricritical point, quadruple critical endpoint, quadruple azeotropic endpoint, quintuple point and critical azeotropic endpoint. The procedure to trace ternary phenomena having two degree of freedom such as critical surface, solid-liquid-vapor surface and liquid-liquid-vapor surface has been discussed. Finally, applications of reliable global methods to solve the fluid-fluid phase equilibrium problem using SAFT equation for binary system and the solid-fluid phase equilibrium problem for binary and ternary systems have been demonstrated through representative computations.
Subjects/Keywords: Automatic differentiation; Homotopy continuation; Critical point; Phase stability; Mathematical modeling; American Studies; Arts and Humanities
Record Details
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Record Details
Similar Records
Cite
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Patel, K. S. (2007). Automatic generation of global phase equilibrium diagram from equation of state. (Thesis). University of South Florida. Retrieved from https://scholarcommons.usf.edu/etd/2318
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Patel, Keyurkumar S. “Automatic generation of global phase equilibrium diagram from equation of state.” 2007. Thesis, University of South Florida. Accessed January 28, 2020.
https://scholarcommons.usf.edu/etd/2318.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Patel, Keyurkumar S. “Automatic generation of global phase equilibrium diagram from equation of state.” 2007. Web. 28 Jan 2020.
Vancouver:
Patel KS. Automatic generation of global phase equilibrium diagram from equation of state. [Internet] [Thesis]. University of South Florida; 2007. [cited 2020 Jan 28].
Available from: https://scholarcommons.usf.edu/etd/2318.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Patel KS. Automatic generation of global phase equilibrium diagram from equation of state. [Thesis]. University of South Florida; 2007. Available from: https://scholarcommons.usf.edu/etd/2318
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
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Open Access Theses and Dissertations
