subject:(saddle point)

University of Delaware

1. Qirko, Klajdi. A Saddle Point Least Squares method for systems of linear PDEs.

Degree: PhD, University of Delaware, Department of Mathematical Sciences, 2017, University of Delaware

URL: http://udspace.udel.edu/handle/19716/23081

► We present a Saddle Point Least Squares (SPLS) method for solving variational formulations with different types of trial and test spaces. The general mixed formulation… (more)

Subjects/Keywords: Pure sciences; PDE; Saddle Point Least Squares

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Qirko, K. (2017). A Saddle Point Least Squares method for systems of linear PDEs. (Doctoral Dissertation). University of Delaware. Retrieved from http://udspace.udel.edu/handle/19716/23081

Chicago Manual of Style (16^th Edition):

Qirko, Klajdi. “A Saddle Point Least Squares method for systems of linear PDEs.” 2017. Doctoral Dissertation, University of Delaware. Accessed March 06, 2021. http://udspace.udel.edu/handle/19716/23081.

MLA Handbook (7^th Edition):

Qirko, Klajdi. “A Saddle Point Least Squares method for systems of linear PDEs.” 2017. Web. 06 Mar 2021.

Vancouver:

Qirko K. A Saddle Point Least Squares method for systems of linear PDEs. [Internet] [Doctoral dissertation]. University of Delaware; 2017. [cited 2021 Mar 06]. Available from: http://udspace.udel.edu/handle/19716/23081.

Council of Science Editors:

Qirko K. A Saddle Point Least Squares method for systems of linear PDEs. [Doctoral Dissertation]. University of Delaware; 2017. Available from: http://udspace.udel.edu/handle/19716/23081

Georgia Tech

2. Rivera Cardoso, Adrian. Advances in online convex optimization, games, and problems with bandit feedback.

Degree: PhD, Industrial and Systems Engineering, 2019, Georgia Tech

URL: http://hdl.handle.net/1853/62724

► In this thesis we study sequential decision making through the lens of Online Learning. Online Learning is a very powerful and general framework for multi-period… (more)

▼ In this thesis we study sequential decision making through the lens of Online Learning. Online Learning is a very powerful and general framework for multi-period decision making. Due to its simple formulation and effectiveness it has become a tool of daily use in multibillion companies. Moreover, due to its beautiful theory and its tight connections with other fields, Online Learning has caught the attention of academics all over the world and driven first-class research. In the first chapter of this thesis, joint work with Huan Xu, we study a problem called: Risk-Averse Convex Bandit. Risk-aversion makes reference to the fact that humans prefer consistent sequences of good rewards instead of highly variable sequences with slightly better rewards. The Risk-Averse Convex Bandit addresses the fact that, while human decision makers are risk-averse, most algorithms for Online Learning are not. In this thesis we provide the first efficient algorithms with strong theoretical guarantees for the Risk-Averse Convex Bandit problem. In the second chapter, joint work with Rachel Cummings, we study the problem of preserving privacy in the setting of online submodular minimization. Submodular functions have multiple applications in machine learning and economics, which usually involve sensitive data from individuals. Using tools from Online Convex Optimization, we provide the first ε-differentially private algorithms for this problem which are almost as good as the non-private versions for this problem. In the third chapter, joint work with Jacob Abernethy, He Wang, and Huan Xu, we study a dynamic version of two player zero-sum games. Zero-sum games are ubiquitous in economics, and central to understanding Linear Programming Duality, Convex and Robust Optimization, and Statistics. For many decades it was thought that one could solve this kind of games using sublinear regret algorithms for Online Convex Optimization. We show that while the previous is true when the game does not change with time, a naive application of these algorithms can be fatal if the game changes and the players are trying to compete with the Nash Equilibrium of the sum of the games in hindsight. In the fourth chapter, joint work with He Wang and Huan Xu, we revisit the decade old problem of Markov Decision Processes (MDPs) with Adversarial Rewards. MDPs provide a general mathematical framework for sequential decision making under uncertainty when there is a notion of `state', moreover they are the backbone of all Reinforcement Learning. We provide an elegant algorithm for this problem using tools from Online Convex Optimization. The algorithm's performance is comparable with current state of the art. We also consider the problem under the large state-space regime, and provide the first algorithm with strong theoretical guarantees. Advisors/Committee Members: Wang, He (advisor), Xu, Huan (advisor), Cummings, Rachel (committee member), Abernethy, Jacob (committee member), Pokutta, Sebastian (committee member).

Subjects/Keywords: Online learning; Zero-sum games; Bandit feedback; Saddle point; Online saddle point; Markov decision process; MDP

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rivera Cardoso, A. (2019). Advances in online convex optimization, games, and problems with bandit feedback. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/62724

Chicago Manual of Style (16^th Edition):

Rivera Cardoso, Adrian. “Advances in online convex optimization, games, and problems with bandit feedback.” 2019. Doctoral Dissertation, Georgia Tech. Accessed March 06, 2021. http://hdl.handle.net/1853/62724.

MLA Handbook (7^th Edition):

Rivera Cardoso, Adrian. “Advances in online convex optimization, games, and problems with bandit feedback.” 2019. Web. 06 Mar 2021.

Vancouver:

Rivera Cardoso A. Advances in online convex optimization, games, and problems with bandit feedback. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1853/62724.

Council of Science Editors:

Rivera Cardoso A. Advances in online convex optimization, games, and problems with bandit feedback. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/62724

Georgia Tech

3. He, Lijuan. Multiple phase transition path and saddle point search in computer aided nano design.

Degree: PhD, Mechanical Engineering, 2015, Georgia Tech

URL: http://hdl.handle.net/1853/53967

► Functional materials with controllable phase transitions have been widely used in devices for information storage (e.g. hard-disk, CD-ROM, memory) and energy storage (e.g. battery, shape… (more)

▼ Functional materials with controllable phase transitions have been widely used in devices for information storage (e.g. hard-disk, CD-ROM, memory) and energy storage (e.g. battery, shape memory alloy). One of the important issues to design such materials is to realize the desirable phase transition processes, in which atomistic simulation can be used for the prediction of materials properties. The accuracy of the prediction is largely dependent on searching the true value of the transition rate, which is determined by the minimum energy barrier between stable states, i.e. the saddle point on a potential energy surface (PES). Although a number of methods that search for saddle points on a PES have been developed, they intend to locate only one saddle point with the maximum energy along the transition path at a time. In addition, they do not consider the input uncertainty associated with the calculation of potential energy. To overcome the limitations, in this dissertation, new saddle point search methods are developed to provide a global view of energy landscape with improved efficiency and robustness. First, a concurrent search algorithm for multiple phase transition pathways is developed. The algorithm is able to search multiple local minima and saddle points simultaneously without prior knowledge of initial and final stable configurations. A new representation of transition paths based on parametric Bézier curves is introduced. A curve subdivision scheme is developed to dynamically locate all the intermediate local minima and saddle points along the transition path. Second, a curve swarm search algorithm is developed to exhaustively locate the local minima and saddle points within a region concurrently. The algorithm is based on the flocking of multiple groups of curves. A collective potential model is built to simulate the communication activities among curves. Third, a hybrid saddle-point search method using stochastic kriging models is developed to improve the efficiency of the search algorithm as well as to incorporate model-form uncertainty and numerical errors associated with density functional theory calculation. These algorithms are demonstrated by predicting the hydrogen diffusion process in FeTiH and body-centered iron Fe8H systems. Advisors/Committee Members: Wang, Yan (advisor), Henkelman, Graeme (committee member), Jang, Seung Soon (committee member), Zhu, Ting (committee member), McDowell, David L. (committee member).

Subjects/Keywords: Saddle point; Reaction path; Density functional theory; Uncertainty

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

He, L. (2015). Multiple phase transition path and saddle point search in computer aided nano design. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/53967

Chicago Manual of Style (16^th Edition):

He, Lijuan. “Multiple phase transition path and saddle point search in computer aided nano design.” 2015. Doctoral Dissertation, Georgia Tech. Accessed March 06, 2021. http://hdl.handle.net/1853/53967.

MLA Handbook (7^th Edition):

He, Lijuan. “Multiple phase transition path and saddle point search in computer aided nano design.” 2015. Web. 06 Mar 2021.

Vancouver:

He L. Multiple phase transition path and saddle point search in computer aided nano design. [Internet] [Doctoral dissertation]. Georgia Tech; 2015. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1853/53967.

Council of Science Editors:

He L. Multiple phase transition path and saddle point search in computer aided nano design. [Doctoral Dissertation]. Georgia Tech; 2015. Available from: http://hdl.handle.net/1853/53967

University of Texas – Austin

4. Duncan, Juliana Rebecca. Simulation methodology for the kinetics of solid state atomic systems.

Degree: PhD, Chemistry, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32439

► A major challenge in computational chemistry and solid-state atomic systems is overcoming the limitations of molecular dynamics (MD) simulations by utilizing alternative methods to efficiently… (more)

▼ A major challenge in computational chemistry and solid-state atomic systems is overcoming the limitations of molecular dynamics (MD) simulations by utilizing alternative methods to efficiently calculate the rate of chemical reactions and diffusion events. The focus of my dissertation is the following: 1) development of new methods to overcome the time scale limitations of MD; 2) greater understanding of the failures of current methods; and 3) application of the current methods to solid-state atomic systems. Harmonic transition state theory (HTST) is a powerful approximation within the transition state theory (TST) framework that reduces the problem of capturing reaction rates to indentifying the lowest energy first order saddle points. In this work, the biased gradient squared descent (BGSD) saddle point finding method is introduced. BGSD first converts all critical points into global minima by transforming the PES into the gradient squared landscape. A biasing term is added to stabilize critical points at a specified energy levels and destabilize other critical points. BGSD is shown to be competitive with the dimer method in terms of force evaluations required to find a set of low-energy saddle points around a reactant minimum. We use adaptive kinetic Monte Carlo simulations to investigate the transformation of a topologically closed packed (TCP) structure to a cubic phase in molybdenum. Molybdenum is one refractory element added to nickel-based superalloys to improve properties of the material for high-temperature applications. However, when the concentrations of refractory elements are too high TCP phases can form and degrade properties of the material. This study is a first step towards an atomistic description of the transformation of TCP phases to cubic phases. A successful method for accelerating MD simulations is Voter's hyperdynamics approach, which adds a non-negative bias potential to the system's potential energy surface (PES). A novel bias potential is introduced which utilizes a machine learning technique and constructs the bias potential based off of the distance to the ridge. The bias potential is shown to produce boost factors, or computational acceleration, that scale well with dimensionality. HTST does a remarkably good job of capturing reaction rates at low temperatures. However, as the temperature increases results generated by HTST can di ffer from direct MD rates by an order of magnitude. The successes and failures of HTST to capture reactions rates are investigated with the goal of inspiring increased accuracy at less cost than other existing methods. Advisors/Committee Members: Henkelman, Graeme (advisor), Makarov, Dmitrii E (committee member), Stanton, John F (committee member), Ganesan, Venkat (committee member), Elber, Ron (committee member), Hwang, Gyeong S (committee member).

Subjects/Keywords: Transition state theory; Saddle point finding; Potential energy surfaces

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Duncan, J. R. (2015). Simulation methodology for the kinetics of solid state atomic systems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32439

Chicago Manual of Style (16^th Edition):

Duncan, Juliana Rebecca. “Simulation methodology for the kinetics of solid state atomic systems.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed March 06, 2021. http://hdl.handle.net/2152/32439.

MLA Handbook (7^th Edition):

Duncan, Juliana Rebecca. “Simulation methodology for the kinetics of solid state atomic systems.” 2015. Web. 06 Mar 2021.

Vancouver:

Duncan JR. Simulation methodology for the kinetics of solid state atomic systems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/2152/32439.

Council of Science Editors:

Duncan JR. Simulation methodology for the kinetics of solid state atomic systems. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32439

NSYSU

5. Hsu, Chung-Kai. Asymptotic Statistics of Channel Capacity for Amplify-and-Forward MIMO Relay Systems.

Degree: Master, Communications Engineering, 2012, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0717112-153556

► In this thesis, we address the statistics of mutual information of amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-hop relay channels, where the source terminal (ST), relay… (more)

Subjects/Keywords: Rayleigh fading; Rician fading; amplify-and-forward relay system; MIMO; saddle-point approximation; superanalysis

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hsu, C. (2012). Asymptotic Statistics of Channel Capacity for Amplify-and-Forward MIMO Relay Systems. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0717112-153556

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Hsu, Chung-Kai. “Asymptotic Statistics of Channel Capacity for Amplify-and-Forward MIMO Relay Systems.” 2012. Thesis, NSYSU. Accessed March 06, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0717112-153556.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Hsu, Chung-Kai. “Asymptotic Statistics of Channel Capacity for Amplify-and-Forward MIMO Relay Systems.” 2012. Web. 06 Mar 2021.

Vancouver:

Hsu C. Asymptotic Statistics of Channel Capacity for Amplify-and-Forward MIMO Relay Systems. [Internet] [Thesis]. NSYSU; 2012. [cited 2021 Mar 06]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0717112-153556.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hsu C. Asymptotic Statistics of Channel Capacity for Amplify-and-Forward MIMO Relay Systems. [Thesis]. NSYSU; 2012. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0717112-153556

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Temple University

6. Ladenheim, Scott Aaron. Constraint Preconditioning of Saddle Point Problems.

Degree: PhD, 2015, Temple University

URL: http://digital.library.temple.edu/u?/p245801coll10,319906

►

Mathematics

This thesis is concerned with the fast iterative solution of linear systems of equations of saddle point form. Saddle point problems are a ubiquitous… (more)

▼

Mathematics

This thesis is concerned with the fast iterative solution of linear systems of equations of saddle point form. Saddle point problems are a ubiquitous class of matrices that arise in a host of computational science and engineering applications. The focus here is on improving the convergence of iterative methods for these problems by preconditioning. Preconditioning is a way to transform a given linear system into a different problem for which iterative methods converge faster. Saddle point matrices have a very specific block structure and many preconditioning strategies for these problems exploit this structure. The preconditioners considered in this thesis are constraint preconditioners. This class of preconditioner mimics the structure of the original saddle point problem. In this thesis, we prove norm- and field-of-values-equivalence for constraint preconditioners associated to saddle point matrices with a particular structure. As a result of these equivalences, the number of iterations needed for convergence of a constraint preconditioned minimal residual Krylov subspace method is bounded, independent of the size of the matrix. In particular, for saddle point systems that arise from the finite element discretization of partial differential equations (p.d.e.s), the number of iterations it takes for GMRES to converge for theses constraint preconditioned systems is bounded (asymptotically), independent of the size of the mesh width. Moreover, we extend these results when appropriate inexact versions of the constraint preconditioner are used. We illustrate this theory by presenting numerical experiments on saddle point matrices that arise from the finite element solution of coupled Stokes-Darcy flow. This is a system of p.d.e.s that models the coupling of a free flow to a porous media flow by conditions across the interface of the two flow regions. We present experiments in both two and three dimensions, using different types of elements (triangular, quadrilateral), different finite element schemes (continuous, discontinuous Galerkin methods), and different geometries. In all cases, the effectiveness of the constraint preconditioner is demonstrated.

Temple University – Theses

Advisors/Committee Members: Szyld, Daniel;, Seibold, Benjamin, Klapper, Isaac, Chidyagwai, Prince;.

Subjects/Keywords: Mathematics;

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ladenheim, S. A. (2015). Constraint Preconditioning of Saddle Point Problems. (Doctoral Dissertation). Temple University. Retrieved from http://digital.library.temple.edu/u?/p245801coll10,319906

Chicago Manual of Style (16^th Edition):

Ladenheim, Scott Aaron. “Constraint Preconditioning of Saddle Point Problems.” 2015. Doctoral Dissertation, Temple University. Accessed March 06, 2021. http://digital.library.temple.edu/u?/p245801coll10,319906.

MLA Handbook (7^th Edition):

Ladenheim, Scott Aaron. “Constraint Preconditioning of Saddle Point Problems.” 2015. Web. 06 Mar 2021.

Vancouver:

Ladenheim SA. Constraint Preconditioning of Saddle Point Problems. [Internet] [Doctoral dissertation]. Temple University; 2015. [cited 2021 Mar 06]. Available from: http://digital.library.temple.edu/u?/p245801coll10,319906.

Council of Science Editors:

Ladenheim SA. Constraint Preconditioning of Saddle Point Problems. [Doctoral Dissertation]. Temple University; 2015. Available from: http://digital.library.temple.edu/u?/p245801coll10,319906

Penn State University

7. Zhang, Jingyan. Shrinking Dimer Dynamics and its Application in Saddle Point Search.

Degree: 2013, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/16848

► The search for saddle point and transition state on an energy surface has broad applications in fields such as materials science, chemistry and biology. In… (more)

▼ The search for saddle point and transition state on an energy surface has broad applications in fields such as materials science, chemistry and biology. In this dissertation, the shrinking dimer dynamics (SDD) and the constrained shrinking dimer dynamics (CSDD) are developed for effective saddle point and transition state search. Both mathematical theory and practical applications of the newly developed methods are presented. Briefly speaking, SDD is a dynamic system which can be applied to locate a transition state on an energy surface corresponding to an index-1 saddle point where the Hessian has a negative eigenvalue. SDD only requires the computation of gradient forces of the energy, thus making it appealing to practical applications. Moreover, by searching for the saddle point and its associated unstable direction simultaneously in a single dynamic system defined in an extended space, we show that unstable index-1 saddle points of the energy become linearly stable steady equilibria of SDD which implies that SDD will likely provide a robust approach for the computation of saddle points. The time discretization of SDD is connected to various iterative algorithms, including the popular dimer method which has been the most widely used approach in the literature for saddle point search. Our study of these discretization schemes lays a rigorous mathematical foundation for corresponding iterative saddle point search algorithms. Both linear local asymptotic stability analysis and optimal error reduction (convergence) rates are presented which are further confirmed by numerical experiments. Global convergence and nonlinear asymptotic stability are also illustrated for some simpler systems. To demonstrate the effectiveness of SDD, results from bench-mark numerical experiments are presented. In addition to the basic form of the SDD, we also consider its variants and extensions, for example, the constrained SDD, or rather, CSDD, which can be used to find index-1 saddle points of an energy function on a constrained manifold. In this dissertation, we also study some applications of SDD and CSDD to interesting problems in both finite and infinite dimensional energy spaces. Examples include a study of critical nuclei morphology in phase transformations, discrete interacting particle systems as described by the generalized Thomson problem, and periodic centroidal Voronoi tessellations. Results of numerical experiments demonstrate how the various parameters used in algorithms affect the performance. They also reveal some findings that are of interests in applications. In non-technical terms, one may view saddle point search from a perspective of mountain hiking. Relatively simple strategies of following a descending path can help a hiker to go down to a bottom of a valley even with no map nor road signs, but getting to the other side of mountain ridge through the right mountain pass (saddle point) requiring much more careful searching. Our work crafts out a strategy for mountain hikers to make correct moves in order… Advisors/Committee Members: Qiang Du, Dissertation Advisor/Co-Advisor, Ludmil Tomov Zikatanov, Committee Member, Xiantao Li, Committee Member, Alexei Novikov, Committee Member, Zhibiao Zhao, Committee Member, Zikui Liu, Committee Member.

Subjects/Keywords: Saddle point search; transition state; Shrinking Dimer Dynamics; dimer method; nucleation; constrained Shrinking Dimer Dynamics

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhang, J. (2013). Shrinking Dimer Dynamics and its Application in Saddle Point Search. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16848

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zhang, Jingyan. “Shrinking Dimer Dynamics and its Application in Saddle Point Search.” 2013. Thesis, Penn State University. Accessed March 06, 2021. https://submit-etda.libraries.psu.edu/catalog/16848.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zhang, Jingyan. “Shrinking Dimer Dynamics and its Application in Saddle Point Search.” 2013. Web. 06 Mar 2021.

Vancouver:

Zhang J. Shrinking Dimer Dynamics and its Application in Saddle Point Search. [Internet] [Thesis]. Penn State University; 2013. [cited 2021 Mar 06]. Available from: https://submit-etda.libraries.psu.edu/catalog/16848.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhang J. Shrinking Dimer Dynamics and its Application in Saddle Point Search. [Thesis]. Penn State University; 2013. Available from: https://submit-etda.libraries.psu.edu/catalog/16848

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

8. Yazdandoost Hamedani, Erfan. Primal-Dual Methods for Saddle-Point Problems with Applications to Decentralized Constrained Convex Optimization.

Degree: 2020, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/17964evy5047

► Saddle-point (SP) problems form an important class of computational problems with the aim of minimizing a function over one variable while maximizing over the other.… (more)

▼ Saddle-point (SP) problems form an important class of computational problems with the aim of minimizing a function over one variable while maximizing over the other. This setting captures a wider class of problems than optimization problems. In particular, when the objective function is convex-concave, it includes convex optimization problems with nonlinear conic constraints as a special case, which itself includes LP, QP, QCQP, SOCP, and SDP as its subclasses. One of the goals of this thesis is to develop efficient and practical first-order methods to solve convex-concave SP problems. The next part of this thesis is dedicated to addressing the challenge of solving distributed optimization problems over communication networks consisting of agents with computational capabilities. In these problems, the information/data are privately owned by the agents and the main goal is for agents to collaboratively find an optimal solution that every agent agrees on by communicating with their neighbors only. Based on the primal-dual method developed in the first part of the thesis, we develop efficient first-order algorithms to solve distributed resource allocation and constrained consensus optimization problems. In the first part, we begin by proposing a primal-dual algorithm with a new momentum term based on partial gradient extrapolation to solve convex-concave SP problems. More importantly, we consider SP problems with a general coupling term that is not assumed to be bilinear; therefore, when compared to the significant majority of related work on primal-dual methods in the literature, our research captures a broader range of SP problems with nonlinear coupling terms, e.g., robust classification, distance metric learning, and kernel matrix learning. One of the main obstacles of implementing first-order algorithms is their dependency on some global parameters that might be unavailable, e.g., Lipschitz constants of the partial gradients. Using a backtracking line-search method we are able to estimate local Lipschitz constants obviating the need for knowing global Lipschitz constants. Through a powerful yet simple analysis, we demonstrate some unified results on the convergence of the proposed method. In particular, we obtain some optimal convergence rate results under both convex and semi-strongly convex settings. In the second part, we then consider cooperative multi-agent resource sharing and consensus optimization problems over both static and time-varying communication networks (with possibly directed edges), where only local communications between neighboring agents are allowed. For both problems, to handle the challenge arising due to time-varying communication networks, the following two key ideas are adopted: (i) A novel formulation of the problem in terms of a consensus set which is independent of the network topology; (ii) Suitably increasing the communication rounds in the course of algorithms to control the error inherited by the disagreements among the nods. More specifically, in a multi-agent resource sharing… Advisors/Committee Members: Necdet S Aybat, Dissertation Advisor/Co-Advisor, Necdet S Aybat, Committee Chair/Co-Chair, Vinayak V Shanbhag, Committee Member, Xingyuan Fang, Committee Member, Constantino Manuel Lagoa, Outside Member, Ling Rothrock, Program Head/Chair.

Subjects/Keywords: saddle-point problem; primal-dual algorithm; decentralized optimization; convex optimization; time-varying network

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Yazdandoost Hamedani, E. (2020). Primal-Dual Methods for Saddle-Point Problems with Applications to Decentralized Constrained Convex Optimization. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/17964evy5047

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yazdandoost Hamedani, Erfan. “Primal-Dual Methods for Saddle-Point Problems with Applications to Decentralized Constrained Convex Optimization.” 2020. Thesis, Penn State University. Accessed March 06, 2021. https://submit-etda.libraries.psu.edu/catalog/17964evy5047.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yazdandoost Hamedani, Erfan. “Primal-Dual Methods for Saddle-Point Problems with Applications to Decentralized Constrained Convex Optimization.” 2020. Web. 06 Mar 2021.

Vancouver:

Yazdandoost Hamedani E. Primal-Dual Methods for Saddle-Point Problems with Applications to Decentralized Constrained Convex Optimization. [Internet] [Thesis]. Penn State University; 2020. [cited 2021 Mar 06]. Available from: https://submit-etda.libraries.psu.edu/catalog/17964evy5047.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yazdandoost Hamedani E. Primal-Dual Methods for Saddle-Point Problems with Applications to Decentralized Constrained Convex Optimization. [Thesis]. Penn State University; 2020. Available from: https://submit-etda.libraries.psu.edu/catalog/17964evy5047

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

9. Nifa, Naoufal. Solveurs performants pour l'optimisation sous contraintes en identification de paramètres : Efficient solvers for constrained optimization in parameter identification problems.

Degree: Docteur es, Génie mécanique, 2017, Université Paris-Saclay (ComUE)

URL: http://www.theses.fr/2017SACLC066

►

Cette thèse vise à concevoir des solveurs efficaces pour résoudre des systèmes linéaires, résultant des problèmes d'optimisation sous contraintes dans certaines applications de dynamique des… (more)

▼

Cette thèse vise à concevoir des solveurs efficaces pour résoudre des systèmes linéaires, résultant des problèmes d'optimisation sous contraintes dans certaines applications de dynamique des structures et vibration (la corrélation calcul-essai, la localisation d'erreur, le modèle hybride, l'évaluation des dommages, etc.). Ces applications reposent sur la résolution de problèmes inverses, exprimés sous la forme de la minimisation d'une fonctionnelle en énergie. Cette fonctionnelle implique à la fois, des données issues d'un modèle numérique éléments finis, et des essais expérimentaux. Ceci conduit à des modèles de haute qualité, mais les systèmes linéaires point-selle associés, sont coûteux à résoudre. Nous proposons deux classes différentes de méthodes pour traiter le système. La première classe repose sur une méthode de factorisation directe profitant de la topologie et des propriétés spéciales de la matrice point-selle. Après une première renumérotation pour regrouper les pivots en blocs d'ordre 2. L'élimination de Gauss est conduite à partir de ces pivots et en utilisant un ordre spécial d'élimination réduisant le remplissage. Les résultats numériques confirment des gains significatifs en terme de remplissage, jusqu'à deux fois meilleurs que la littérature pour la topologie étudiée. La seconde classe de solveurs propose une approche à double projection du système étudié sur le noyau des contraintes, en faisant une distinction entre les contraintes cinématiques et celles reliées aux capteurs sur la structure. La première projection est explicite en utilisant une base creuse du noyau. La deuxième est implicite. Elle est basée sur l'emploi d'un préconditionneur contraint avec des méthodes itératives de type Krylov. Différentes approximations des blocs du préconditionneur sont proposées. L'approche est implémentée dans un environnement distribué parallèle utilisant la bibliothèque PETSc. Des gains significatifs en terme de coût de calcul et de mémoire sont illustrés sur plusieurs applications industrielles.

This thesis aims at designing efficient numerical solution methods to solve linear systems, arising in constrained optimization problems in some structural dynamics and vibration applications (test-analysis correlation, model error localization,hybrid model, damage assessment, etc.). These applications rely on solving inverse problems, by means of minimization of an energy-based functional. This latter involves both data from a numerical finite element model and from experimental tests, which leads to high quality models, but the associated linear systems, that have a saddle-point coefficient matrices, are long and costly to solve. We propose two different classes of methods to deal with these problems. First, a direct factorization method that takes advantage of the special structures and properties of these saddle point matrices. The Gaussian elimination factorization is implemented in order to factorize the saddle point matrices block-wise with small blocks of orders 2 and using a fill-in reducing topological…

Advisors/Committee Members: Aubry, Denis (thesis director).

Subjects/Keywords: Optimisation sous contraintes; Systèmes point-Selle; Préconditionneurs par blocs; Problèmes inverses; Constrained optimization; Saddle point systems; Block preconditioners; Inverse problems

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Nifa, N. (2017). Solveurs performants pour l'optimisation sous contraintes en identification de paramètres : Efficient solvers for constrained optimization in parameter identification problems. (Doctoral Dissertation). Université Paris-Saclay (ComUE). Retrieved from http://www.theses.fr/2017SACLC066

Chicago Manual of Style (16^th Edition):

Nifa, Naoufal. “Solveurs performants pour l'optimisation sous contraintes en identification de paramètres : Efficient solvers for constrained optimization in parameter identification problems.” 2017. Doctoral Dissertation, Université Paris-Saclay (ComUE). Accessed March 06, 2021. http://www.theses.fr/2017SACLC066.

MLA Handbook (7^th Edition):

Nifa, Naoufal. “Solveurs performants pour l'optimisation sous contraintes en identification de paramètres : Efficient solvers for constrained optimization in parameter identification problems.” 2017. Web. 06 Mar 2021.

Vancouver:

Nifa N. Solveurs performants pour l'optimisation sous contraintes en identification de paramètres : Efficient solvers for constrained optimization in parameter identification problems. [Internet] [Doctoral dissertation]. Université Paris-Saclay (ComUE); 2017. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2017SACLC066.

Council of Science Editors:

Nifa N. Solveurs performants pour l'optimisation sous contraintes en identification de paramètres : Efficient solvers for constrained optimization in parameter identification problems. [Doctoral Dissertation]. Université Paris-Saclay (ComUE); 2017. Available from: http://www.theses.fr/2017SACLC066

10. Badahmane, Achraf. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.

Degree: Docteur es, Mathématiques. Mathématiques appliquées, 2019, Littoral; Université Cadi Ayyad (Marrakech, Maroc)

URL: http://www.theses.fr/2019DUNK0543

►

La résolution numérique des problèmes de point-selle a eu une attention particulière ces dernières années. À titre d'exemple, la mécanique des fluides et solides conduit… (more)

Subjects/Keywords: Point-selle; Préconditionnement; Krylov; Produit de Kronecker; Produit de diamant; Saddle point; Preconditioner; Global Krylov subspace method; Kronecker product; Diamond product

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Badahmane, A. (2019). Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. (Doctoral Dissertation). Littoral; Université Cadi Ayyad (Marrakech, Maroc). Retrieved from http://www.theses.fr/2019DUNK0543

Chicago Manual of Style (16^th Edition):

Badahmane, Achraf. “Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.” 2019. Doctoral Dissertation, Littoral; Université Cadi Ayyad (Marrakech, Maroc). Accessed March 06, 2021. http://www.theses.fr/2019DUNK0543.

MLA Handbook (7^th Edition):

Badahmane, Achraf. “Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides.” 2019. Web. 06 Mar 2021.

Vancouver:

Badahmane A. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. [Internet] [Doctoral dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2019. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2019DUNK0543.

Council of Science Editors:

Badahmane A. Méthodes de sous espaces de Krylov préconditionnées pour les problèmes de point-selle avec plusieurs seconds membres : Preconditioned global Krylov subspace methods for solving saddle point problems with multiple right-hand sides. [Doctoral Dissertation]. Littoral; Université Cadi Ayyad (Marrakech, Maroc); 2019. Available from: http://www.theses.fr/2019DUNK0543

11. Louka, Maria. Επαναληπτικές μέθοδοι για την αριθμητική επίλυση γραμμικών συστημάτων.

Degree: 2011, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)

URL: http://hdl.handle.net/10442/hedi/33466

►

The objective of this thesis is the design and analysis of iterative methods for the numerical solution of large and sparse linear systems. This type… (more)

▼

The objective of this thesis is the design and analysis of iterative methods for the numerical solution of large and sparse linear systems. This type of systems emerge from the discretization of Partial Differential Equations. Two special categories of linear systems are studied. The first category contains systems whose coefficient matrix is two cyclic whereas the second category includes the augmented linear systems. Initially, the Preconditioned Simultaneous Displacement (PSD) method is studied when the Jacobi iteration matrix is weakly cyclic and its eigenvalues are all real "real case" or all imaginary "imaginary case". It is proved that the PSD method has better convergence rate than the SSOR method. In particular, in the "imaginary case" its convergence is increased by an order of magnitude. In an attempt to further increase the convergence rate of the PSD method, more parameters were introduced. The new method is called the Modified PSD (MPSD) method. Under the same assumptions the convergence of the MPSD method is studied. It is shown that the optimum MPSD method is equivalent to the optimum MSOR method. Furthermore, it is studied the convergence analysis of the Generalized Modified Extrapolated SOR (GMESOR) and Generalized Modified Preconditioned Simultaneous Displacement (GMPSD) methods for the numerical solution of the augmented linear systems. The main result of our analysis is that both methods have the same rate of convergence and less complexity than the Preconditioned Conjugate Gradient (PCG) method. The last result is important since it proves that the addition of parameters in an iterative method incurs the same increase in the rate of convergence as that of the Conjugate Gradient (CG) method which belongs to the Krylov subspace methods.

Ο αντικειμενικός σκοπός της διδακτορικής διατριβής αφορά τον σχεδιασμό και την ανάλυση επαναληπτικών μεθόδων για την αριθμητική επίλυση μεγάλων και αραιών γραμμικών συστημάτων. Συστήματα με αυτά τα χαρακτηριστικά προκύπτουν από τη διακριτοποίηση Μερικών Dιαφορικών Εξισώσεων. Μελετώνται δύο ειδικές κατηγορίες συστημάτων. Η πρώτη κατηγορία περιλαμβάνει συστήματα των οποίων ο πίνακας συντελεστών των αγνώστων είναι δικυκλικός ενώ ή δεύτερη περιέχει τα επαυξημένα (augmented) συστήματα. Στη διδακτορική διατριβή μελετάται αρχικά η σύγκλιση της Preconditioned Simultaneous Displacement (PSD) μεθόδου, όταν ο επαναληπτικός πίνακας Jacobi είναι ασθενά κυκλικός με τις ιδιοτιμές του να είναι είτε όλες πραγματικές ¨πραγματική περίπτωση¨ είτε όλες Φανταστικές ¨φανταστική περίπτωση¨ και αποδεικνύεται ότι η ταχύτητα σύγκλισής της είναι μεγαλύτερη από εκείνη της SSOR μεθόδου. Ειδικά στη ¨φανταστική περίπτωση¨ η σύγκλισή της βελτιώνεται κατά μια τάξη μεγέθους. Σε μια προσπάθεια περαιτέρω αύξησης της ταχύτητας σύγκλισης της PSD μεθόδου, εισήχθησαν περισσότερες παράμετροι. Η νέα μέθοδος που δημιουργήθηκε ονομάστηκε Modified PSD (MPSD). Κάτω από τις ίδιες υποθέσεις μελετήθηκε η σύγκλιση της MPSD μεθόδου. Το κύριο αποτέλεσμα της ανάλυσης αυτής είναι ότι η MPSD μέθοδος καθίσταται…

Subjects/Keywords: Επαναληπτικές μέθοδοι; Δικυκλικοί πίνακες; Γραμμικά συστήματα; Πρόβλημα σαγματικού σημείου; SOR; Iterative methods; Twocyclic matrices; Linear systems; Saddle point problem; SOR

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Louka, M. (2011). Επαναληπτικές μέθοδοι για την αριθμητική επίλυση γραμμικών συστημάτων. (Thesis). National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Retrieved from http://hdl.handle.net/10442/hedi/33466

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Louka, Maria. “Επαναληπτικές μέθοδοι για την αριθμητική επίλυση γραμμικών συστημάτων.” 2011. Thesis, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Accessed March 06, 2021. http://hdl.handle.net/10442/hedi/33466.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Louka, Maria. “Επαναληπτικές μέθοδοι για την αριθμητική επίλυση γραμμικών συστημάτων.” 2011. Web. 06 Mar 2021.

Vancouver:

Louka M. Επαναληπτικές μέθοδοι για την αριθμητική επίλυση γραμμικών συστημάτων. [Internet] [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2011. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10442/hedi/33466.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Louka M. Επαναληπτικές μέθοδοι για την αριθμητική επίλυση γραμμικών συστημάτων. [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2011. Available from: http://hdl.handle.net/10442/hedi/33466

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universidade Estadual de Campinas

12. Mendes, Douglas, 1985-. Um método de espaço nulo livre de bases para a resolução de problemas de ponto-de-sela simétricos e generalizados: A basis-free null space method for solving symmetric and generalized saddle point problems.

Degree: 2016, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/321702

► Abstract: In this thesis we use an augmented Lagrangian matrix approach to determine the exact solutions of a broad class of linear systems composed by… (more)

▼ Abstract: In this thesis we use an augmented Lagrangian matrix approach to determine the exact solutions of a broad class of linear systems composed by symmetric and nonsymmetric saddle point problems. Some mild assumptions are made to this end and a preconditioning is specially designed to decrease the sensitivity of the linear systems before the calculation of their solutions. In this way, the expressions found can be properly employed for computational purposes in a large number of applications. As an example of such a procedure, we develop a direct method for solving symmetric saddle point problems. Then we show that this method is intrinsically related with the null space method, but it doesn't depend on finding a basis to the null space of the latter. For this reason, we say the proposed method is a basis-free null space method. This method is also extended to a direct method for the solving of generalized saddle point problems, for which we can also freely make the same statements. To the best of our knowledge, there isn't any specific direct method for the solving of the last problems. So little their exact solution is known in the literature. Thus it is of major interest, since it can lead to the development of efficient algorithms, besides our own. Lastly, we explicit the expression of the inverse of the coefficient matrix of the nonsymmetric systems, also not know in the literature, and we identify the weakest possible assumptions that are needed to guarantee the solvability of all the saddle point problems considered here, once again obtaining new results Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Ehrhardt, Maria Aparecida Diniz, 1956- (advisor), Pedroso, Lucas Garcia (coadvisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution), Programa de Pós-Graduação em Matemática Aplicada (nameofprogram), Ruggiero, Márcia Aparecida Gomes (committee member), Correa, Maicon Ribeiro (committee member), Matioli, Luiz Carlos (committee member), Bueno, Luís Felipe Cesar da Rocha (committee member).

Subjects/Keywords: Sistemas ponto de sela; Soluções exatas; Métodos numéricos; Pré-condicionadores; Saddle point systems; Exact solutions; Numerical methods; Preconditioners

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mendes, Douglas, 1. (2016). Um método de espaço nulo livre de bases para a resolução de problemas de ponto-de-sela simétricos e generalizados: A basis-free null space method for solving symmetric and generalized saddle point problems. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/321702

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mendes, Douglas, 1985-. “Um método de espaço nulo livre de bases para a resolução de problemas de ponto-de-sela simétricos e generalizados: A basis-free null space method for solving symmetric and generalized saddle point problems.” 2016. Thesis, Universidade Estadual de Campinas. Accessed March 06, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/321702.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mendes, Douglas, 1985-. “Um método de espaço nulo livre de bases para a resolução de problemas de ponto-de-sela simétricos e generalizados: A basis-free null space method for solving symmetric and generalized saddle point problems.” 2016. Web. 06 Mar 2021.

Vancouver:

Mendes, Douglas 1. Um método de espaço nulo livre de bases para a resolução de problemas de ponto-de-sela simétricos e generalizados: A basis-free null space method for solving symmetric and generalized saddle point problems. [Internet] [Thesis]. Universidade Estadual de Campinas; 2016. [cited 2021 Mar 06]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/321702.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mendes, Douglas 1. Um método de espaço nulo livre de bases para a resolução de problemas de ponto-de-sela simétricos e generalizados: A basis-free null space method for solving symmetric and generalized saddle point problems. [Thesis]. Universidade Estadual de Campinas; 2016. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/321702

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Stellenbosch University

13. Buitendag, Sven. The saddle-point method and its application to the hill estimator.

Degree: MCom, Statistics, 2016, Stellenbosch University

URL: http://hdl.handle.net/10019.1/100057

►

ENGLISH SUMMARY : The saddle-point approximation is a highly accurate approximation of the distribution of a random variable. It was originally derived as an approximation… (more)

Subjects/Keywords: Saddle point method (Numerical analysis); Hill estimator; Method of steepest descent (Numerical analysis); Edgeworth expansions; Extreme value theory; UCTD

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Buitendag, S. (2016). The saddle-point method and its application to the hill estimator. (Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/100057

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Buitendag, Sven. “The saddle-point method and its application to the hill estimator.” 2016. Thesis, Stellenbosch University. Accessed March 06, 2021. http://hdl.handle.net/10019.1/100057.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Buitendag, Sven. “The saddle-point method and its application to the hill estimator.” 2016. Web. 06 Mar 2021.

Vancouver:

Buitendag S. The saddle-point method and its application to the hill estimator. [Internet] [Thesis]. Stellenbosch University; 2016. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10019.1/100057.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Buitendag S. The saddle-point method and its application to the hill estimator. [Thesis]. Stellenbosch University; 2016. Available from: http://hdl.handle.net/10019.1/100057

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Texas A&M University

14. Ghesmati, Arezou. Residual and Goal-Oriented h- and hp-adaptive Finite Element; Application for Elliptic and Saddle Point Problems.

Degree: PhD, Mathematics, 2018, Texas A&M University

URL: http://hdl.handle.net/1969.1/173289

► We propose and implement an automatic hp-adaptive refinement algorithm for the Stokes model problem. In this work, the strategy is based on the earlier work… (more)

▼ We propose and implement an automatic hp-adaptive refinement algorithm for the Stokes model problem. In this work, the strategy is based on the earlier work done by Dörfler at al. in 2007 for the Poisson problem. Similar to any other adaptivity approach, an a posteriori estimator is needed to control the error in areas with high residuals. We define a family of residual-based estimators Ŋva a € [0; 1] for the hp-adaptive finite element approximation of the exact solution. Moreover, we show the reliability and efficiency of the estimators Ŋva. Finally, numerical examples illustrate the exponential convergence rate of the hp-AFEM in comparison with the h-AFEM. In many applications, such as analysis of fluid flows in our case, we are not interested in computing the solution itself, but instead the aim is finding a good approximation for some functional of interest. In these cases, the idea is to develop some a posteriori error estimates to generate a sequence of h- or hp-adaptive grids that minimize the error in our goal functional with respect to the problem size. In this work, we apply local averaging interpolation operators such as Scott-Zhang and Clément type operators to formulate the dual weight of our proposed goal-oriented error estimator. This idea was recently used in an application to the Poisson problem. We extend those results to saddle-point problems and provide a dual-weighted goal estimator for each cell. The reliability of the goal estimator is proved and numerical examples demonstrate the performance of the locally defined dual-weighted goal-estimator in terms of reliability, efficiency, and convergence. Another important aspect of this research is providing a goal-oriented adaptive finite element method for symmetric second-order linear elliptic problems. We prove that the product of primal and dual estimators, which is a reliable upper bound for the error in the goal functional, decays at the optimal rate. The results reported in the numerical experiments confirm the quasi-optimality behavior of our goal-oriented algorithm. Advisors/Committee Members: Bangerth, Wolfgang (advisor), Guermond, Jean Luc (committee member), Bonito, Andrea (committee member), Ragusa, Jean C (committee member).

Subjects/Keywords: Adaptive Finite Elements; Elliptic Problems; Saddle Point Problems; Goal-Oriented Adaptivity; Aposteriori Error Estimate; Optimal Convergence Rate

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ghesmati, A. (2018). Residual and Goal-Oriented h- and hp-adaptive Finite Element; Application for Elliptic and Saddle Point Problems. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/173289

Chicago Manual of Style (16^th Edition):

Ghesmati, Arezou. “Residual and Goal-Oriented h- and hp-adaptive Finite Element; Application for Elliptic and Saddle Point Problems.” 2018. Doctoral Dissertation, Texas A&M University. Accessed March 06, 2021. http://hdl.handle.net/1969.1/173289.

MLA Handbook (7^th Edition):

Ghesmati, Arezou. “Residual and Goal-Oriented h- and hp-adaptive Finite Element; Application for Elliptic and Saddle Point Problems.” 2018. Web. 06 Mar 2021.

Vancouver:

Ghesmati A. Residual and Goal-Oriented h- and hp-adaptive Finite Element; Application for Elliptic and Saddle Point Problems. [Internet] [Doctoral dissertation]. Texas A&M University; 2018. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1969.1/173289.

Council of Science Editors:

Ghesmati A. Residual and Goal-Oriented h- and hp-adaptive Finite Element; Application for Elliptic and Saddle Point Problems. [Doctoral Dissertation]. Texas A&M University; 2018. Available from: http://hdl.handle.net/1969.1/173289

Texas A&M University

15. Wang, Jieyu. Ultrashort Pulse Propagation in the Linear Regime.

Degree: MS, Physics, 2010, Texas A&M University

URL: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7362

► First, we investigate the Bouguer-Lambert-Beer (BLB) law as applied to the transmission of ultrashort pulses through water in the linear absorption regime. We present a… (more)

Subjects/Keywords: Ultrashort pulse; Precursor; Saddle point method; GVD

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wang, J. (2010). Ultrashort Pulse Propagation in the Linear Regime. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7362

Chicago Manual of Style (16^th Edition):

Wang, Jieyu. “Ultrashort Pulse Propagation in the Linear Regime.” 2010. Masters Thesis, Texas A&M University. Accessed March 06, 2021. http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7362.

MLA Handbook (7^th Edition):

Wang, Jieyu. “Ultrashort Pulse Propagation in the Linear Regime.” 2010. Web. 06 Mar 2021.

Vancouver:

Wang J. Ultrashort Pulse Propagation in the Linear Regime. [Internet] [Masters thesis]. Texas A&M University; 2010. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7362.

Council of Science Editors:

Wang J. Ultrashort Pulse Propagation in the Linear Regime. [Masters Thesis]. Texas A&M University; 2010. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7362

McMaster University

16. Song, Lin. Gaussian Robust Sequential and Predictive Coding.

Degree: PhD, 2012, McMaster University

URL: http://hdl.handle.net/11375/12396

►

Video coding schemes designed based on sequential or predictive coding models are vulnerable to the loss of encoded frames at the decoder end. Motivated… (more)

Subjects/Keywords: Extremal inequality; Gauss-Markov source; minimax theorem; predictive coding; saddle point; sequential coding; Electrical and Electronics; Electrical and Electronics

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Song, L. (2012). Gaussian Robust Sequential and Predictive Coding. (Doctoral Dissertation). McMaster University. Retrieved from http://hdl.handle.net/11375/12396

Chicago Manual of Style (16^th Edition):

Song, Lin. “Gaussian Robust Sequential and Predictive Coding.” 2012. Doctoral Dissertation, McMaster University. Accessed March 06, 2021. http://hdl.handle.net/11375/12396.

MLA Handbook (7^th Edition):

Song, Lin. “Gaussian Robust Sequential and Predictive Coding.” 2012. Web. 06 Mar 2021.

Vancouver:

Song L. Gaussian Robust Sequential and Predictive Coding. [Internet] [Doctoral dissertation]. McMaster University; 2012. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/11375/12396.

Council of Science Editors:

Song L. Gaussian Robust Sequential and Predictive Coding. [Doctoral Dissertation]. McMaster University; 2012. Available from: http://hdl.handle.net/11375/12396

University of Manchester

17. Newsum, Craig. Efficient reduced basis methods for parameter-dependent saddle point problems.

Degree: PhD, 2019, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/efficient-reduced-basis-methods-for-parameterdependent-saddle-point-problems(c9fe675e-42b2-4306-a05c-b6b7ad96de8f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.771491

► We are interested in the efficient numerical solution of parameter-dependent saddle point problems arising from discretisations of systems of PDEs with uncertain inputs. Two popular… (more)

▼ We are interested in the efficient numerical solution of parameter-dependent saddle point problems arising from discretisations of systems of PDEs with uncertain inputs. Two popular solution strategies for such problems are stochastic collocation mixed finite element methods and stochastic Galerkin mixed finite element methods. The former requires the solution of a long sequence of deterministic linear systems corresponding to different choices of the input parameters while the latter requires the solution of a single extremely large linear system. Typically, a fine spatial discretisation is required, and this can lead to large discrete problems that are extremely time and memory intensive to solve. These are significant bottlenecks in the forward propagation of uncertainty in PDE models. Reduced basis methods (RBMs) seek to overcome these bottlenecks by reducing the size of the so-called high fidelity problem through a projection onto a lower-dimensional space. The dimension of this space should be large enough so that the corresponding reduced solution is sufficiently accurate but small enough that the reduced problem is cheaper to solve. There are two novel contributions in this thesis. First, we develop an efficient RBM algorithm to reduce the computational costs associated with stochastic collocation mixed finite element methods. For saddle point problems, we need to construct two reduced spaces which must be compatible to provide a well-posed reduced problem. This is done in a potentially expensive offline stage. We also use a discrete empirical interpolation method (DEIM) to approximate the uncertain inputs as these may depend non-affinely on the input parameters. We are then able to solve the sequence of linear systems at a dramatically cheaper cost. In addition, our algorithm is faster than the standard greedy algorithm for constructing the reduced spaces. Second, we develop an efficient solution algorithm for solving the huge saddle point systems arising from stochastic Galerkin mixed finite element methods in cases where there is not enough memory to use standard Krylov subspace methods. Our approach uses ideas from rational Krylov subspace approximation to iteratively generate a reduced approximation space. This strategy provides a low-rank approximation to the solution of the stochastic Galerkin equations which can be obtained at a much lower cost and using less memory when compared to standard preconditioned iterative methods. Both of the new reduced basis algorithms proposed in this thesis allow for the efficient forward propagation of uncertainty in PDE models. We demonstrate the extent of savings achieved through comprehensive numerical experiments.

Subjects/Keywords: 510; PDEs with random inputs; Saddle point problems; Stochastic collocation; Stochastic Galerkin; Uncertainty quantification; Reduced basis methods

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Newsum, C. (2019). Efficient reduced basis methods for parameter-dependent saddle point problems. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/efficient-reduced-basis-methods-for-parameterdependent-saddle-point-problems(c9fe675e-42b2-4306-a05c-b6b7ad96de8f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.771491

Chicago Manual of Style (16^th Edition):

Newsum, Craig. “Efficient reduced basis methods for parameter-dependent saddle point problems.” 2019. Doctoral Dissertation, University of Manchester. Accessed March 06, 2021. https://www.research.manchester.ac.uk/portal/en/theses/efficient-reduced-basis-methods-for-parameterdependent-saddle-point-problems(c9fe675e-42b2-4306-a05c-b6b7ad96de8f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.771491.

MLA Handbook (7^th Edition):

Newsum, Craig. “Efficient reduced basis methods for parameter-dependent saddle point problems.” 2019. Web. 06 Mar 2021.

Vancouver:

Newsum C. Efficient reduced basis methods for parameter-dependent saddle point problems. [Internet] [Doctoral dissertation]. University of Manchester; 2019. [cited 2021 Mar 06]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/efficient-reduced-basis-methods-for-parameterdependent-saddle-point-problems(c9fe675e-42b2-4306-a05c-b6b7ad96de8f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.771491.

Council of Science Editors:

Newsum C. Efficient reduced basis methods for parameter-dependent saddle point problems. [Doctoral Dissertation]. University of Manchester; 2019. Available from: https://www.research.manchester.ac.uk/portal/en/theses/efficient-reduced-basis-methods-for-parameterdependent-saddle-point-problems(c9fe675e-42b2-4306-a05c-b6b7ad96de8f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.771491

Delft University of Technology

18. Van Turnhout, M. A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design.

Degree: 2009, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90

► A major problem in optical system design is that the optical merit function landscape is usually very complicated, especially for complex design problems where many… (more)

Subjects/Keywords: optical system design; saddle point; optimization; fractal; chaos

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Van Turnhout, M. (2009). A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90

Chicago Manual of Style (16^th Edition):

Van Turnhout, M. “A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design.” 2009. Doctoral Dissertation, Delft University of Technology. Accessed March 06, 2021. http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90.

MLA Handbook (7^th Edition):

Van Turnhout, M. “A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design.” 2009. Web. 06 Mar 2021.

Vancouver:

Van Turnhout M. A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design. [Internet] [Doctoral dissertation]. Delft University of Technology; 2009. [cited 2021 Mar 06]. Available from: http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90.

Council of Science Editors:

Van Turnhout M. A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design. [Doctoral Dissertation]. Delft University of Technology; 2009. Available from: http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; urn:NBN:nl:ui:24-uuid:6c6197bd-5757-428a-9d3d-e94af148ce90 ; http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90

Georgia Tech

19. Lai, Kevin A. Convergence in Min-Max Optimization.

Degree: PhD, Computer Science, 2020, Georgia Tech

URL: http://hdl.handle.net/1853/62809

► Min-max optimization is a classic problem with applications in constrained optimization, robust optimization, and game theory. This dissertation covers new convergence rate results in min-max… (more)

Subjects/Keywords: Optimization; Zero-sum game; Game theory; Fictitious play; Generative adversarial networks; Last-iterate; Min-max; Saddle point

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lai, K. A. (2020). Convergence in Min-Max Optimization. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/62809

Chicago Manual of Style (16^th Edition):

Lai, Kevin A. “Convergence in Min-Max Optimization.” 2020. Doctoral Dissertation, Georgia Tech. Accessed March 06, 2021. http://hdl.handle.net/1853/62809.

MLA Handbook (7^th Edition):

Lai, Kevin A. “Convergence in Min-Max Optimization.” 2020. Web. 06 Mar 2021.

Vancouver:

Lai KA. Convergence in Min-Max Optimization. [Internet] [Doctoral dissertation]. Georgia Tech; 2020. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1853/62809.

Council of Science Editors:

Lai KA. Convergence in Min-Max Optimization. [Doctoral Dissertation]. Georgia Tech; 2020. Available from: http://hdl.handle.net/1853/62809

Brigham Young University

20. Hettikankanange, Praneeth Madushan. Varying the Aspect Ratio of Toroidal Ion Traps: Implications for Design, Performance, and Miniaturization.

Degree: MS, 2020, Brigham Young University

URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9734&context=etd

► A large aspect ratio leads to higher ion capacity in miniaturized ion trap mass spectrometers. The aspect ratio (AR) of an ion trap represents… (more)

Subjects/Keywords: Toroidal Ion Trap; Aspect ratio; Saddle point; Geometric center; Higher-order multipoles; Secular frequency; Physical Sciences and Mathematics

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hettikankanange, P. M. (2020). Varying the Aspect Ratio of Toroidal Ion Traps: Implications for Design, Performance, and Miniaturization. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9734&context=etd

Chicago Manual of Style (16^th Edition):

Hettikankanange, Praneeth Madushan. “Varying the Aspect Ratio of Toroidal Ion Traps: Implications for Design, Performance, and Miniaturization.” 2020. Masters Thesis, Brigham Young University. Accessed March 06, 2021. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9734&context=etd.

MLA Handbook (7^th Edition):

Hettikankanange, Praneeth Madushan. “Varying the Aspect Ratio of Toroidal Ion Traps: Implications for Design, Performance, and Miniaturization.” 2020. Web. 06 Mar 2021.

Vancouver:

Hettikankanange PM. Varying the Aspect Ratio of Toroidal Ion Traps: Implications for Design, Performance, and Miniaturization. [Internet] [Masters thesis]. Brigham Young University; 2020. [cited 2021 Mar 06]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9734&context=etd.

Council of Science Editors:

Hettikankanange PM. Varying the Aspect Ratio of Toroidal Ion Traps: Implications for Design, Performance, and Miniaturization. [Masters Thesis]. Brigham Young University; 2020. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9734&context=etd

21. Penet, Maxime. Robust Nonlinear Model Predictive Control based on Constrained Saddle Point Optimization : Stability Analysis and Application to Type 1 Diabetes : Commande Prédictive Nonlinéaire Robuste par Méthode de Point Selle en Optimisation sous Contraintes : Analyse de Stabilité et Application au Diabète de Type 1.

Degree: Docteur es, Automatique (STIC), 2013, Supélec

URL: http://www.theses.fr/2013SUPL0019

►

Cette thèse s’intéresse au développement d’un contrôleur sûre et robuste en tant que partie intégrante d’un pancréas artificiel. Plus précisément, nous sommes intéressés à contrôler… (more)

▼

Cette thèse s’intéresse au développement d’un contrôleur sûre et robuste en tant que partie intégrante d’un pancréas artificiel. Plus précisément, nous sommes intéressés à contrôler la partie du traitement usuel qui a pour but d’équilibrer la glycémie du patient. C’est ainsi que le développement d’une commande prédictive nonlinéaire robuste basée sur la résolution d’un problème de point selle a été envisagé. Afin de valider les performances du contrôleur dans une situation réaliste, des simulations numériques en utilisant une plate-forme de tests validée par la FDA sont envisagées.Dans une première partie, nous présentons une extension de la classique commande prédictive nonlinéaire dont le but est d’assurer le contrôle robuste de systèmes décrits par des équations différentielles ordinaires non linéaires dans un cadre échantillonné. Ce contrôleur, qui calcule une action de contrôle adéquate en considérant la solution d’un problème de point selle, est appelé saddle point model predictive controller (SPMPC). En utilisant cette commande, il est prouvé que le système converge en temps fini dans un espace borné et, en supposant une certaine structure dans le problème, qu’il est pratiquement stable entrée-état. Ensuite, nous nous sommes intéressés à la résolution numérique. Pour ce faire, nous proposons une méthode de résolution inspirée de la méthode du Langrangien augmenté et qui fait usage de modèles adjoints.Dans un deuxième temps, nous considérons l’application de ce contrôleur au problème du contrôle artificiel de la glycémie. Après une phase de modélisation, nous avons retenu deux modèles : un modèle simple qui est utilisé pour développer la commande et un modèle complexe qui est utilisé comme un simulateur réaliste de patients. Ce dernier est nécessaire pour valider notre approche de contrôle. Afin de calculer une entrée de commande adéquate, la commande SPMPC a besoin de l’état complet du système. Or, les capteurs ne peuvent fournir qu’une valeur du glucose sanguin. C’est pourquoi le développement d’un observateur est envisagé. Ensuite, des simulations sont réalisées. Les résultats obtenus témoignent de l’intérêt de l’approche retenue. En effet, pour tous les patients, aucune hypoglycémie n’a été observée et le temps passé en état hyperglycémique est suffisamment faible pour ne pas être dommageable. Enfin, l’intérêt d’étendre l’approche de commande SPMPC au problème de contrôle de systèmes décrits par des équations différentielles retardées non linéaires dans un cadre échantillonné est formellement investigué.

This thesis deals with the design of a robust and safe control algorithm to aim at an artificial pancreas. More precisely we will be interested in controlling the stabilizing part of a classical cure. To meet this objective, the design of a robust nonlinear model predictive controller based on the solution of a saddle point optimization problem is considered. Also, to test the controller performances in a realistic case, numerical simulations on a FDA validated testing platform are envisaged.In a first…

Advisors/Committee Members: Guéguen, Hervé (thesis director).

Subjects/Keywords: Contrôle robuste; Point selle; Modèle adjoint; NMPC; Diabète de type 1; Robust control; Saddle point; Adjoint model; NMPC; Type 1 diabetes; 378.242

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Penet, M. (2013). Robust Nonlinear Model Predictive Control based on Constrained Saddle Point Optimization : Stability Analysis and Application to Type 1 Diabetes : Commande Prédictive Nonlinéaire Robuste par Méthode de Point Selle en Optimisation sous Contraintes : Analyse de Stabilité et Application au Diabète de Type 1. (Doctoral Dissertation). Supélec. Retrieved from http://www.theses.fr/2013SUPL0019

Chicago Manual of Style (16^th Edition):

Penet, Maxime. “Robust Nonlinear Model Predictive Control based on Constrained Saddle Point Optimization : Stability Analysis and Application to Type 1 Diabetes : Commande Prédictive Nonlinéaire Robuste par Méthode de Point Selle en Optimisation sous Contraintes : Analyse de Stabilité et Application au Diabète de Type 1.” 2013. Doctoral Dissertation, Supélec. Accessed March 06, 2021. http://www.theses.fr/2013SUPL0019.

MLA Handbook (7^th Edition):

Penet, Maxime. “Robust Nonlinear Model Predictive Control based on Constrained Saddle Point Optimization : Stability Analysis and Application to Type 1 Diabetes : Commande Prédictive Nonlinéaire Robuste par Méthode de Point Selle en Optimisation sous Contraintes : Analyse de Stabilité et Application au Diabète de Type 1.” 2013. Web. 06 Mar 2021.

Vancouver:

Penet M. Robust Nonlinear Model Predictive Control based on Constrained Saddle Point Optimization : Stability Analysis and Application to Type 1 Diabetes : Commande Prédictive Nonlinéaire Robuste par Méthode de Point Selle en Optimisation sous Contraintes : Analyse de Stabilité et Application au Diabète de Type 1. [Internet] [Doctoral dissertation]. Supélec; 2013. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2013SUPL0019.

Council of Science Editors:

Penet M. Robust Nonlinear Model Predictive Control based on Constrained Saddle Point Optimization : Stability Analysis and Application to Type 1 Diabetes : Commande Prédictive Nonlinéaire Robuste par Méthode de Point Selle en Optimisation sous Contraintes : Analyse de Stabilité et Application au Diabète de Type 1. [Doctoral Dissertation]. Supélec; 2013. Available from: http://www.theses.fr/2013SUPL0019

22. Lemaire, Simon. Discrétisations non-conformes d'un modèle poromécanique sur maillages généraux : Nonconforming discretizations of a poromechanical model on general meshes.

Degree: Docteur es, Mathématiques, 2013, Université Paris-Est

URL: http://www.theses.fr/2013PEST1168

►

Cette thèse s'intéresse à la conception de méthodes de discrétisation non-conforme pour un modèle de poromécanique. Le but de ce travail est de simplifier les… (more)

▼

Cette thèse s'intéresse à la conception de méthodes de discrétisation non-conforme pour un modèle de poromécanique. Le but de ce travail est de simplifier les couplages liant la géomécanique d'un milieu poreux à l'écoulement polyphasique compositionnel ayant cours en son sein tels qu'ils sont réalisés actuellement dans l'industrie pétrolière, en discrétisant sur un même maillage, typiquement non-conforme car à l'image de la lithologie, la mécanique et l'écoulement. La nouveauté consiste donc à traiter la mécanique par une méthode d'approximation non-conforme sur maillages généraux. Dans cette thèse, nous nous concentrons sur un modèle d'élasticité linéaire. Les difficultés inhérentes à son approximation non-conforme sont son manque de coercivité (se traduisant par la nécessité de satisfaire une inégalité de Korn sur un espace discret discontinu), ainsi que le phénomène de verrouillage numérique lorsque le matériau tend à devenir incompressible. Dans une première partie, nous construisons un espace d'approximation sur maillages généraux, s'apparentant à une extension de l'espace de Crouzeix-Raviart. Nous explicitons ses propriétés d'approximation et de conformité, et montrons que ce dernier est adapté à une discrétisation primale coercive et robuste au locking du modèle d'élasticité sur maillages généraux. La méthode proposée est moins coûteuse que son équivalent éléments finis (en termes de propriétés) P2. Nous nous intéressons dans une deuxième partie à l'approximation non-conforme d'un modèle couplé de poroélasticité. Nous étudions la convergence d'une famille de schémas numériques dont la discrétisation en espace utilise le formalisme des schémas Gradient, auquel appartient la méthode développée pour la mécanique. Nous prouvons la convergence de telles approximations vers la solution de régularité minimale du problème continu, indépendamment des paramètres physiques du système

This manuscript focuses on the conception of nonconforming discretization methods for a poromechanical model. The aim of this work is to ease the coupling between the geomechanics and the multiphase compositional Darcy flow in porous media by discretizing mechanics and flow on the same mesh, typically nonconforming as it represents the lithology. Hence, the novelty hinges on a nonconforming treatment of mechanics on general meshes. In this work, we focus on a linear elasticity model. The nonconforming approximation of such a model is not straightforward owing to its lack of coercivity (meaning that a discrete Korn's inequality must hold on a discontinuous discrete space) and to the numerical locking phenomenon occurring as the material becomes incompressible. In a first part, we design an approximation space on general meshes, which can be viewed as an extension of the so-called Crouzeix-Raviart space. We study its approximation and conformity properties, and prove that this latter is well-adapted to the design of a primal, coercive, and locking-free discretization of the elasticity model on general meshes. The proposed method is less…

Advisors/Committee Members: Eymard, Robert (thesis director).

Subjects/Keywords: Poroélasticité; Méthodes non-conformes; Maillages généraux; Volumes finis; Verrouillage numérique; Problèmes de point-selle; Poroelasticity; Nonconforming methods; General meshes; Finite volumes; Numerical locking; Saddle-point problems

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lemaire, S. (2013). Discrétisations non-conformes d'un modèle poromécanique sur maillages généraux : Nonconforming discretizations of a poromechanical model on general meshes. (Doctoral Dissertation). Université Paris-Est. Retrieved from http://www.theses.fr/2013PEST1168

Chicago Manual of Style (16^th Edition):

Lemaire, Simon. “Discrétisations non-conformes d'un modèle poromécanique sur maillages généraux : Nonconforming discretizations of a poromechanical model on general meshes.” 2013. Doctoral Dissertation, Université Paris-Est. Accessed March 06, 2021. http://www.theses.fr/2013PEST1168.

MLA Handbook (7^th Edition):

Lemaire, Simon. “Discrétisations non-conformes d'un modèle poromécanique sur maillages généraux : Nonconforming discretizations of a poromechanical model on general meshes.” 2013. Web. 06 Mar 2021.

Vancouver:

Lemaire S. Discrétisations non-conformes d'un modèle poromécanique sur maillages généraux : Nonconforming discretizations of a poromechanical model on general meshes. [Internet] [Doctoral dissertation]. Université Paris-Est; 2013. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2013PEST1168.

Council of Science Editors:

Lemaire S. Discrétisations non-conformes d'un modèle poromécanique sur maillages généraux : Nonconforming discretizations of a poromechanical model on general meshes. [Doctoral Dissertation]. Université Paris-Est; 2013. Available from: http://www.theses.fr/2013PEST1168

Queensland University of Technology

23. Kempthorne, Daryl Matthew. The development of virtual leaf surface models for interactive agrichemical spray applications.

Degree: 2015, Queensland University of Technology

URL: http://eprints.qut.edu.au/84525/

► This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton,… (more)

Subjects/Keywords: digitisation; 3D scanning; virtual leaf reconstruction; surface fitting; discrete smoothing D2 splines; thin plate spline finite element method; preconditioning saddle point problems; parameterisation techniques

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kempthorne, D. M. (2015). The development of virtual leaf surface models for interactive agrichemical spray applications. (Thesis). Queensland University of Technology. Retrieved from http://eprints.qut.edu.au/84525/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kempthorne, Daryl Matthew. “The development of virtual leaf surface models for interactive agrichemical spray applications.” 2015. Thesis, Queensland University of Technology. Accessed March 06, 2021. http://eprints.qut.edu.au/84525/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kempthorne, Daryl Matthew. “The development of virtual leaf surface models for interactive agrichemical spray applications.” 2015. Web. 06 Mar 2021.

Vancouver:

Kempthorne DM. The development of virtual leaf surface models for interactive agrichemical spray applications. [Internet] [Thesis]. Queensland University of Technology; 2015. [cited 2021 Mar 06]. Available from: http://eprints.qut.edu.au/84525/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kempthorne DM. The development of virtual leaf surface models for interactive agrichemical spray applications. [Thesis]. Queensland University of Technology; 2015. Available from: http://eprints.qut.edu.au/84525/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

24. Rejane dos Santos Brito. Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante.

Degree: 2009, Universidade Federal Rural de Pernambuco

URL: http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321

►

Inicialmente, realiza-se uma revisão literária sobre as expansões assintóticas de Daniels, Edgeworth, Lugannani-Rice e Cordeiro-Ferrari. Mediante uso da expansão de Cordeiro- Ferrari, torna-se possível realizar… (more)

Subjects/Keywords: Distribuições beta generalizadas; Aproximação ponto de sela; Distribuição beta power; Regressão logística; Análise discriminante; Ciências Agrárias; Biometria; Saddle Point Approximation; Generalized Beta Distribution; Beta Power Distribution; Logistic Regression; Discriminant Analysis

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Brito, R. d. S. (2009). Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante. (Thesis). Universidade Federal Rural de Pernambuco. Retrieved from http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Brito, Rejane dos Santos. “Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante.” 2009. Thesis, Universidade Federal Rural de Pernambuco. Accessed March 06, 2021. http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Brito, Rejane dos Santos. “Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante.” 2009. Web. 06 Mar 2021.

Vancouver:

Brito RdS. Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante. [Internet] [Thesis]. Universidade Federal Rural de Pernambuco; 2009. [cited 2021 Mar 06]. Available from: http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Brito RdS. Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante. [Thesis]. Universidade Federal Rural de Pernambuco; 2009. Available from: http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

25. Rejane dos Santos Brito. Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante.

Degree: 2009, Universidade Federal Rural de Pernambuco

URL: http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321

►

Inicialmente, realiza-se uma revisão literária sobre as expansões assintóticas de Daniels, Edgeworth, Lugannani-Rice e Cordeiro-Ferrari. Mediante uso da expansão de Cordeiro- Ferrari, torna-se possível realizar… (more)

Subjects/Keywords: Distribuições beta generalizadas; Análise discriminante; Generalized Beta Distribution; Logistic Regression; Saddle Point Approximation; Ciências Agrárias; Biometria; Distribuição beta power; Regressão logística; Aproximação ponto de sela; Beta Power Distribution; Discriminant Analysis

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Brito, R. d. S. (2009). Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante. (Thesis). Universidade Federal Rural de Pernambuco. Retrieved from http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Brito, Rejane dos Santos. “Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante.” 2009. Thesis, Universidade Federal Rural de Pernambuco. Accessed March 06, 2021. http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Brito, Rejane dos Santos. “Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante.” 2009. Web. 06 Mar 2021.

Vancouver:

Brito RdS. Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante. [Internet] [Thesis]. Universidade Federal Rural de Pernambuco; 2009. [cited 2021 Mar 06]. Available from: http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Brito RdS. Estudo de expansões assintóticas, avaliação numérica de momentos das distribuições beta generalizadas, aplicações em modelos de regressão e análise discriminante. [Thesis]. Universidade Federal Rural de Pernambuco; 2009. Available from: http://200.17.137.108/tde_busca/arquivo.php?codArquivo=321

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. Rossato, Rafael Antonio. Sistemas elípticos de tipo hamiltoniano perto da ressonância.

Degree: PhD, Matemática, 2014, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042015-164728/ ;

►

Neste trabalho consideramos sistemas elípticos de tipo hamiltoniano, envolvendo o operador Laplaciano, com uma parte linear dependendo de dois parâmetros e uma perturbação sublinear. Obtemos… (more)

Subjects/Keywords: Aproximação finito dimensional; Finite dimensional approximation; Geometria de ponto de sela; Near resonance problems; Problemas de quase ressonância; Saddle point geometry; Semilinear elliptic systems; Sistemas elípticos semilineares

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rossato, R. A. (2014). Sistemas elípticos de tipo hamiltoniano perto da ressonância. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042015-164728/ ;

Chicago Manual of Style (16^th Edition):

Rossato, Rafael Antonio. “Sistemas elípticos de tipo hamiltoniano perto da ressonância.” 2014. Doctoral Dissertation, University of São Paulo. Accessed March 06, 2021. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042015-164728/ ;.

MLA Handbook (7^th Edition):

Rossato, Rafael Antonio. “Sistemas elípticos de tipo hamiltoniano perto da ressonância.” 2014. Web. 06 Mar 2021.

Vancouver:

Rossato RA. Sistemas elípticos de tipo hamiltoniano perto da ressonância. [Internet] [Doctoral dissertation]. University of São Paulo; 2014. [cited 2021 Mar 06]. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042015-164728/ ;.

Council of Science Editors:

Rossato RA. Sistemas elípticos de tipo hamiltoniano perto da ressonância. [Doctoral Dissertation]. University of São Paulo; 2014. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042015-164728/ ;

27. A. Fiscella. VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS.

Degree: 2014, Università degli Studi di Milano

URL: http://hdl.handle.net/2434/245334

► My thesis deals with nonlinear elliptic problems involving a non-local integrodifferential operator of fractional type. Our main results concern the existence of weak solutions for… (more)

Subjects/Keywords: integrodifferential operators; fractional Laplacian; Saddle Point Theorem; Palais-Smale condition; Stationary Kirchhoff problems; critical nonlinearities; variational methods; Settore MAT/05 - Analisi Matematica

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Fiscella, A. (2014). VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS. (Thesis). Università degli Studi di Milano. Retrieved from http://hdl.handle.net/2434/245334

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Fiscella, A.. “VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS.” 2014. Thesis, Università degli Studi di Milano. Accessed March 06, 2021. http://hdl.handle.net/2434/245334.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Fiscella, A.. “VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS.” 2014. Web. 06 Mar 2021.

Vancouver:

Fiscella A. VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS. [Internet] [Thesis]. Università degli Studi di Milano; 2014. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/2434/245334.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Fiscella A. VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS. [Thesis]. Università degli Studi di Milano; 2014. Available from: http://hdl.handle.net/2434/245334

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

28. Ul Jabbar, Absaar. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.

Degree: 2018, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-19859

► Multigrid methods belong to the best-known methods for solving linear systems arising from the discretization of elliptic partial differential equations. The main attraction of multigrid… (more)

▼ Multigrid methods belong to the best-known methods for solving linear systems arising from the discretization of elliptic partial differential equations. The main attraction of multigrid methods is that they have an asymptotically meshindependent convergence behavior. Multigrid with Vanka (or local multilevel pressure Schur complement method) as smoother have been frequently used for the construction of very effcient coupled monolithic solvers for the solution of the stationary incompressible Navier-Stokes equations in 2D and 3D. However, due to its innate Gauß-Seidel/Jacobi character, Vanka has a strong influence of the underlying mesh, and therefore, coupled multigrid solvers with Vanka smoothing very frequently face convergence issues on meshes with high aspect ratios. Moreover, even on very nice regular grids, these solvers may fail when the anisotropies are introduced from the differential operator. In this thesis, we develop a new class of robust and efficient monolithic finite element multilevel Krylov subspace methods (MLKM) for the solution of the stationary incompressible Navier-Stokes equations as an alternative to the coupled multigrid-based solvers. Different from multigrid, the MLKM utilizes a Krylov method as the basis in the error reduction process. The solver is based on the multilevel projection-based method of Erlangga and Nabben, which accelerates the convergence of the Krylov subspace methods by shifting the small eigenvalues of the system matrix, responsible for the slow convergence of the Krylov iteration, to the largest eigenvalue. Before embarking on the Navier-Stokes equations, we first test our implementation of the MLKM solver by solving scalar model problems, namely the convection-diffusion problem and the anisotropic diffusion problem. We validate the method by solving several standard benchmark problems. Next, we present the numerical results for the solution of the incompressible Navier-Stokes equations in two dimensions. The results show that the MLKM solvers produce asymptotically mesh-size independent, as well as Reynolds number independent convergence rates, for a moderate range of Reynolds numbers. Moreover, numerical simulations also show that the coupled MLKM solvers can handle (both mesh and operator based) anisotropies better than the coupled multigrid solvers. Advisors/Committee Members: Turek, Stefan (advisor), Blum, Heribert (referee).

Subjects/Keywords: Monolithic multilevel methods; Krylov subspaces; GMRES; FEM; Navier-Stokes equations; Saddle point problems; 510; Multi-level-Verfahren; Krylov-Verfahren; Finite-Elemente-Methode; Navier-Stokes-Gleichung

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ul Jabbar, A. (2018). Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-19859

Chicago Manual of Style (16^th Edition):

Ul Jabbar, Absaar. “Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.” 2018. Doctoral Dissertation, Technische Universität Dortmund. Accessed March 06, 2021. http://dx.doi.org/10.17877/DE290R-19859.

MLA Handbook (7^th Edition):

Ul Jabbar, Absaar. “Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations.” 2018. Web. 06 Mar 2021.

Vancouver:

Ul Jabbar A. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2018. [cited 2021 Mar 06]. Available from: http://dx.doi.org/10.17877/DE290R-19859.

Council of Science Editors:

Ul Jabbar A. Efficient and robust monolithic finite element multilevel Krylov subspace solvers for the solution of stationary incompressible Navier-Stokes equations. [Doctoral Dissertation]. Technische Universität Dortmund; 2018. Available from: http://dx.doi.org/10.17877/DE290R-19859

Freie Universität Berlin

29. Gräser, Carsten. Konvexe Minimierung und Phasenfeldmodelle.

Degree: 2011, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-11584

► Phasenfeldmodelle sind ein weit verbreiteter Ansatz zur Beschreibung von Prozessen, die sich wesentlich durch dünne Interfaceregionen zwischen weitestgehend homogenen Bereichen auszeichnen. Ein wichtiges Anwendungsfeld von… (more)

▼ Phasenfeldmodelle sind ein weit verbreiteter Ansatz zur Beschreibung von Prozessen, die sich wesentlich durch dünne Interfaceregionen zwischen weitestgehend homogenen Bereichen auszeichnen. Ein wichtiges Anwendungsfeld von Phasenfeldmodellen ist die Modellierung von physikalischen Phasenübergangs- und Phasenseparationvorgängen. Eine wesentliche Eigenschaften ist dabei, dass die Trennung der Phasen durch ein Doppelmuldenpotential getrieben ist, welches voneinander getrennte Minima für jede Phase besitzt. Bereits 1958 haben Cahn und Hilliard ein logarithmisches Potential vorgeschlagen, das zwar differenzierbar ist, aber singuläre Ableitungen besitzt. Geht die Temperatur gegen Null, so degeneriert das temperaturabhängige logarithmische Potential gegen das nichtdifferenzierbare Hindernispotential. Ziel der vorliegenden Arbeit ist die Entwicklung von Methoden zur effizienten numerischen Lösung solcher Gleichungen, die auch im Fall nichtglatter Potentiale und anisotroper Oberflächenenergien robust sind. Diese Methoden werden für die Cahn-Hilliard-Gleichung entwickelt, die prototypisch für eine Vielzahl solcher Modelle ist. Das Hauptresultat der Arbeit ist die Entwicklung eines schnellen iterativen Verfahrens zur Lösung nichtlinearer Sattelpunktprobleme, wie sie bei der Diskretisierung anisotroper Cahn-Hilliard-Gleichungen mit Finite-Elemente-Methoden entstehen. Die Grundlage dieses Verfahrens ist eine Umformulierung des Sattelpunktproblems als äquivalentes duales Minimierungsproblem. Das Energiefunktional dieses Minimierungsproblems ist differenzierbar und seine Ableitung ist das nichtlineare Schur-Komplement des Sattelpunktproblems. Für dieses Schur- Komplement wird eine verallgemeinerte Linearisierung hergeleitet, die im Rahmen eines nichtglatten Newton-Verfahrens Verwendung findet. Für dieses so genannte "Schur Nonsmooth Newton" Verfahren wird die globale Konvergenz mittels der Äquivalenz zu Abstiegsverfahren für das duale Minimierungsproblem gezeigt. Ferner wird bewiesen, dass die globale Konvergenz auch bei inexaktem Lösen der linearen Newton Probleme erhalten bleibt. In jedem Schritt dieses Verfahrens ist ein nichtlineares konvexes Minimierungsproblem zu lösen. Für die effiziente Behandlung dieser Teilprobleme wird das so genannte "Truncated Nonsmooth Newton Multigrid" (TNNMG) Verfahren entwickelt. Dieses nichtlineare Mehrgitterverfahren zeichnet sich im Gegensatz zu verwandten Verfahren durch seine Einfachheit und die Anwendbarkeit auf anisotrope Probleme aus. Hinsichtlich der Konvergenzgeschwindigkeit ist es bereits bekannten Verfahren ebenbürtig. Numerische Beispiele zeigen, dass die entwickelten Verfahren gitterunabhängig konvergieren. Auch erweisen sich die Verfahren als robust für verschiedene Temperaturen, einschließlich dem Grenzfall Null. Der Grund für diese Robustheit ist, dass die Verfahren nicht auf Differenzierbarkeit sondern der konvexen Struktur der Probleme basieren. Advisors/Committee Members: [email protected] (contact), m (gender), Prof. Dr. Ralf Kornhuber (firstReferee), Prof. Dr. Charles M. Elliott (furtherReferee).

Subjects/Keywords: phase field models; Cahn-Hilliard equation; convex minimization; nonsmooth Newton method; multigrid; saddle point problems; 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gräser, C. (2011). Konvexe Minimierung und Phasenfeldmodelle. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-11584

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gräser, Carsten. “Konvexe Minimierung und Phasenfeldmodelle.” 2011. Thesis, Freie Universität Berlin. Accessed March 06, 2021. http://dx.doi.org/10.17169/refubium-11584.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gräser, Carsten. “Konvexe Minimierung und Phasenfeldmodelle.” 2011. Web. 06 Mar 2021.

Vancouver:

Gräser C. Konvexe Minimierung und Phasenfeldmodelle. [Internet] [Thesis]. Freie Universität Berlin; 2011. [cited 2021 Mar 06]. Available from: http://dx.doi.org/10.17169/refubium-11584.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gräser C. Konvexe Minimierung und Phasenfeldmodelle. [Thesis]. Freie Universität Berlin; 2011. Available from: http://dx.doi.org/10.17169/refubium-11584

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oxford

30. Pearson, John W. Fast iterative solvers for PDE-constrained optimization problems.

Degree: PhD, 2013, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:316e54dc-0623-4063-b9c3-1012c62ac83a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405

► In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we… (more)

Subjects/Keywords: 518; Mathematics; Numerical analysis; Calculus of variations and optimal control; Partial differential equations; numerical linear algebra; preconditioning; PDE-constrained optimization; saddle point systems

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Pearson, J. W. (2013). Fast iterative solvers for PDE-constrained optimization problems. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:316e54dc-0623-4063-b9c3-1012c62ac83a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405

Chicago Manual of Style (16^th Edition):

Pearson, John W. “Fast iterative solvers for PDE-constrained optimization problems.” 2013. Doctoral Dissertation, University of Oxford. Accessed March 06, 2021. http://ora.ox.ac.uk/objects/uuid:316e54dc-0623-4063-b9c3-1012c62ac83a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405.

MLA Handbook (7^th Edition):

Pearson, John W. “Fast iterative solvers for PDE-constrained optimization problems.” 2013. Web. 06 Mar 2021.

Vancouver:

Pearson JW. Fast iterative solvers for PDE-constrained optimization problems. [Internet] [Doctoral dissertation]. University of Oxford; 2013. [cited 2021 Mar 06]. Available from: http://ora.ox.ac.uk/objects/uuid:316e54dc-0623-4063-b9c3-1012c62ac83a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405.

Council of Science Editors:

Pearson JW. Fast iterative solvers for PDE-constrained optimization problems. [Doctoral Dissertation]. University of Oxford; 2013. Available from: http://ora.ox.ac.uk/objects/uuid:316e54dc-0623-4063-b9c3-1012c62ac83a ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405

		in
And / Or
		in
And / Or
		in
And / Or
		in

Open Access Theses and Dissertations