subject:(Preconditioner)

Temple University

1. Du, Xiuhong. Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG.

Degree: PhD, 2008, Temple University

URL: http://digital.library.temple.edu/u?/p245801coll10,6474

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Mathematics

The GMRES method is a widely used iterative method for solving the linear systems, of the form Ax = b, especially for the solution… (more)

Subjects/Keywords: Mathematics; Preconditioner; GMRES; CG; Inexact

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APA (6^th Edition):

Du, X. (2008). Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG. (Doctoral Dissertation). Temple University. Retrieved from http://digital.library.temple.edu/u?/p245801coll10,6474

Chicago Manual of Style (16^th Edition):

Du, Xiuhong. “Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG.” 2008. Doctoral Dissertation, Temple University. Accessed April 15, 2021. http://digital.library.temple.edu/u?/p245801coll10,6474.

MLA Handbook (7^th Edition):

Du, Xiuhong. “Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG.” 2008. Web. 15 Apr 2021.

Vancouver:

Du X. Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG. [Internet] [Doctoral dissertation]. Temple University; 2008. [cited 2021 Apr 15]. Available from: http://digital.library.temple.edu/u?/p245801coll10,6474.

Council of Science Editors:

Du X. Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG. [Doctoral Dissertation]. Temple University; 2008. Available from: http://digital.library.temple.edu/u?/p245801coll10,6474

Delft University of Technology

2. Pouw, Dennis (author). Implementation direct solver to allow for better preconditioners in iterative solver.

Degree: 2021, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:c8a59633-d29d-4dfd-94c0-1bd4a78e7992

► In order to decrease the time that the viscous-flow solver PARNASSOS needs to simulate ship-generated waves, direct solvers are introduced in order to make the… (more)

Subjects/Keywords: Preconditioner; Viscous flow simulations; MARIN

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APA (6^th Edition):

Pouw, D. (. (2021). Implementation direct solver to allow for better preconditioners in iterative solver. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:c8a59633-d29d-4dfd-94c0-1bd4a78e7992

Chicago Manual of Style (16^th Edition):

Pouw, Dennis (author). “Implementation direct solver to allow for better preconditioners in iterative solver.” 2021. Masters Thesis, Delft University of Technology. Accessed April 15, 2021. http://resolver.tudelft.nl/uuid:c8a59633-d29d-4dfd-94c0-1bd4a78e7992.

MLA Handbook (7^th Edition):

Pouw, Dennis (author). “Implementation direct solver to allow for better preconditioners in iterative solver.” 2021. Web. 15 Apr 2021.

Vancouver:

Pouw D(. Implementation direct solver to allow for better preconditioners in iterative solver. [Internet] [Masters thesis]. Delft University of Technology; 2021. [cited 2021 Apr 15]. Available from: http://resolver.tudelft.nl/uuid:c8a59633-d29d-4dfd-94c0-1bd4a78e7992.

Council of Science Editors:

Pouw D(. Implementation direct solver to allow for better preconditioners in iterative solver. [Masters Thesis]. Delft University of Technology; 2021. Available from: http://resolver.tudelft.nl/uuid:c8a59633-d29d-4dfd-94c0-1bd4a78e7992

Penn State University

3. Yang, Kai. Stable discretization and robust preconditioning for fluid-structure interaction.

Degree: 2015, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/26333

► In the simulation of multiphysics systems, we often encounter large-scale linear systems arising from the implicit time discretizations of coupled PDEs. Although it is possible… (more)

Subjects/Keywords: fluid-structure interaction; poroelasticity; block preconditioner

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APA (6^th Edition):

Yang, K. (2015). Stable discretization and robust preconditioning for fluid-structure interaction. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/26333

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):

Yang, Kai. “Stable discretization and robust preconditioning for fluid-structure interaction.” 2015. Thesis, Penn State University. Accessed April 15, 2021. https://submit-etda.libraries.psu.edu/catalog/26333.

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

MLA Handbook (7^th Edition):

Yang, Kai. “Stable discretization and robust preconditioning for fluid-structure interaction.” 2015. Web. 15 Apr 2021.

Vancouver:

Yang K. Stable discretization and robust preconditioning for fluid-structure interaction. [Internet] [Thesis]. Penn State University; 2015. [cited 2021 Apr 15]. Available from: https://submit-etda.libraries.psu.edu/catalog/26333.

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

Council of Science Editors:

Yang K. Stable discretization and robust preconditioning for fluid-structure interaction. [Thesis]. Penn State University; 2015. Available from: https://submit-etda.libraries.psu.edu/catalog/26333

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

4. Clarke, Lauren. Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times.

Degree: MS, Chemical Engineering, 2018, University of North Dakota

URL: https://commons.und.edu/theses/2189

► A computational bottleneck during the solution to multiphase formulations of the incompressible Navier-Stokes equations is often during the implicit solution of the pressure-correction equation… (more)

▼ A computational bottleneck during the solution to multiphase formulations of the incompressible Navier-Stokes equations is often during the implicit solution of the pressure-correction equation that results from operator-splitting methods. Since density is a coefficient in the pressure-correction equation, large variations or discontinuities among the phase densities greatly increase the condition number of the pressure-correction matrix and impede the convergence of iterative methods employed in its solution. To alleviate this shortcoming, the open-source multiphase code MFiX is interfaced with the linear solver library PETSc. Through an appropriate mapping of matrix and vector data structures between the two software, the access to a suite of robust, scalable, solver options in PETSc is obtained. Verification of the implementation of MFiX-PETSc is demonstrated through predictions that are identical to those obtained from MFiXâs native solvers for a simple heat conduction case with a well-known solution. After verifying the framework, several cases were tested with MFiX-PETSc to analyze the performance of various solver and preconditioner combinations. For a low Reynolds number, flow over a cylinder case, applying right-side Block Jacobi preconditioning to the BiCGSTAB iterative solver in MFiX-PETSc was 28-40% faster than MFiXâs native solver at the finest mesh resolution. Similarly, the left-side Block Jacobi preconditioner in MFiX-PETSc was 27â46% faster for the same fine meshing. Further assessments of these preconditioning options were then made for a fluidized bed problem involving different bed geometries, convergence tolerances, material densities, and inlet velocities. For a three-dimensional geometry with uniform meshing, native MFiX was faster than MFiX-PETSc for each simulation. The difference in speed was minimized when a low density fluidization material (polypropylene) was used along with a higher order discretization scheme. With these settings, MFiX-PETSc was only 2-6% slower than native MFiX when right-side Block Jacobi preconditioning was employed. The fluidized bed was then represented by a two-dimensional geometry with fine meshing towards the center. When this bed was filled with glass beads, right-side Block Jacobi was 28% faster than MFiXâs native solver, which was the largest speedup encountered throughout this 2D case. Advisors/Committee Members: Gautham Krishnamoorthy.

Subjects/Keywords: BiCGSTAB; CFD; MFiX; Multiphase flow; PETSc; Preconditioner

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APA (6^th Edition):

Clarke, L. (2018). Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times. (Masters Thesis). University of North Dakota. Retrieved from https://commons.und.edu/theses/2189

Chicago Manual of Style (16^th Edition):

Clarke, Lauren. “Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times.” 2018. Masters Thesis, University of North Dakota. Accessed April 15, 2021. https://commons.und.edu/theses/2189.

MLA Handbook (7^th Edition):

Clarke, Lauren. “Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times.” 2018. Web. 15 Apr 2021.

Vancouver:

Clarke L. Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times. [Internet] [Masters thesis]. University of North Dakota; 2018. [cited 2021 Apr 15]. Available from: https://commons.und.edu/theses/2189.

Council of Science Editors:

Clarke L. Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times. [Masters Thesis]. University of North Dakota; 2018. Available from: https://commons.und.edu/theses/2189

University of South Carolina

5. DENG, XIAODI. A Fast Preconditioner For Helmholtz Equation.

Degree: MS, Mathematics, 2012, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/1591

This monograph implements a fast preconditioner of Helmholtz Equation and a related GMRES iterative algorithm. Numerical results are listed and several thoughts and considerations are included. Advisors/Committee Members: Qi Wang.

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; helmholtz; preconditioner

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APA (6^th Edition):

DENG, X. (2012). A Fast Preconditioner For Helmholtz Equation. (Masters Thesis). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/1591

Chicago Manual of Style (16^th Edition):

DENG, XIAODI. “A Fast Preconditioner For Helmholtz Equation.” 2012. Masters Thesis, University of South Carolina. Accessed April 15, 2021. https://scholarcommons.sc.edu/etd/1591.

MLA Handbook (7^th Edition):

DENG, XIAODI. “A Fast Preconditioner For Helmholtz Equation.” 2012. Web. 15 Apr 2021.

Vancouver:

DENG X. A Fast Preconditioner For Helmholtz Equation. [Internet] [Masters thesis]. University of South Carolina; 2012. [cited 2021 Apr 15]. Available from: https://scholarcommons.sc.edu/etd/1591.

Council of Science Editors:

DENG X. A Fast Preconditioner For Helmholtz Equation. [Masters Thesis]. University of South Carolina; 2012. Available from: https://scholarcommons.sc.edu/etd/1591

Texas State University – San Marcos

6. Salit, Robert. A Fast Solver for the Expanded Mixed Finite Element Method.

Degree: MS, Applied Mathematics, 2018, Texas State University – San Marcos

URL: https://digital.library.txstate.edu/handle/10877/8504

► We present a fast solver for expanded mixed finite element method with a discontinuous coefficient. Our result is based on the auxiliary space preconditioning method… (more)

Subjects/Keywords: Finite element method; Preconditioner; Fast solver

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APA (6^th Edition):

Salit, R. (2018). A Fast Solver for the Expanded Mixed Finite Element Method. (Masters Thesis). Texas State University – San Marcos. Retrieved from https://digital.library.txstate.edu/handle/10877/8504

Chicago Manual of Style (16^th Edition):

Salit, Robert. “A Fast Solver for the Expanded Mixed Finite Element Method.” 2018. Masters Thesis, Texas State University – San Marcos. Accessed April 15, 2021. https://digital.library.txstate.edu/handle/10877/8504.

MLA Handbook (7^th Edition):

Salit, Robert. “A Fast Solver for the Expanded Mixed Finite Element Method.” 2018. Web. 15 Apr 2021.

Vancouver:

Salit R. A Fast Solver for the Expanded Mixed Finite Element Method. [Internet] [Masters thesis]. Texas State University – San Marcos; 2018. [cited 2021 Apr 15]. Available from: https://digital.library.txstate.edu/handle/10877/8504.

Council of Science Editors:

Salit R. A Fast Solver for the Expanded Mixed Finite Element Method. [Masters Thesis]. Texas State University – San Marcos; 2018. Available from: https://digital.library.txstate.edu/handle/10877/8504

University of Manchester

7. White, Raymon. Parallel block preconditioning of the incompressible Navier-Stokes equations with weakly imposed boundary conditions.

Degree: PhD, 2016, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/parallel-block-preconditioning-of-the-incompressible-navierstokes-equations-with-weakly-imposed-boundary-conditions(c52883a7-1349-4955-8917-14a85c7bd174).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727867

► This project is concerned with the development and implementation of a novel preconditioning method for the iterative solution of linear systems that arise in the… (more)

Subjects/Keywords: 005.1; Block Preconditioner; OOMPH-LIB; C++; Parallel Programming; Linear Solver; Preconditioner; Iterative Linear Solver; Navier-Stokes; Boundary Conditions

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

APA (6^th Edition):

White, R. (2016). Parallel block preconditioning of the incompressible Navier-Stokes equations with weakly imposed boundary conditions. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/parallel-block-preconditioning-of-the-incompressible-navierstokes-equations-with-weakly-imposed-boundary-conditions(c52883a7-1349-4955-8917-14a85c7bd174).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727867

Chicago Manual of Style (16^th Edition):

White, Raymon. “Parallel block preconditioning of the incompressible Navier-Stokes equations with weakly imposed boundary conditions.” 2016. Doctoral Dissertation, University of Manchester. Accessed April 15, 2021. https://www.research.manchester.ac.uk/portal/en/theses/parallel-block-preconditioning-of-the-incompressible-navierstokes-equations-with-weakly-imposed-boundary-conditions(c52883a7-1349-4955-8917-14a85c7bd174).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727867.

MLA Handbook (7^th Edition):

White, Raymon. “Parallel block preconditioning of the incompressible Navier-Stokes equations with weakly imposed boundary conditions.” 2016. Web. 15 Apr 2021.

Vancouver:

White R. Parallel block preconditioning of the incompressible Navier-Stokes equations with weakly imposed boundary conditions. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2021 Apr 15]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/parallel-block-preconditioning-of-the-incompressible-navierstokes-equations-with-weakly-imposed-boundary-conditions(c52883a7-1349-4955-8917-14a85c7bd174).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727867.

Council of Science Editors:

White R. Parallel block preconditioning of the incompressible Navier-Stokes equations with weakly imposed boundary conditions. [Doctoral Dissertation]. University of Manchester; 2016. Available from: https://www.research.manchester.ac.uk/portal/en/theses/parallel-block-preconditioning-of-the-incompressible-navierstokes-equations-with-weakly-imposed-boundary-conditions(c52883a7-1349-4955-8917-14a85c7bd174).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727867

University of Manchester

8. White, Raymon. Parallel Block Preconditioning of the Incompressible Navier-Stokes Equations with Weakly Imposed Boundary Conditions.

Degree: 2016, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:305538

►

This project is concerned with the development and implementation of a novel preconditioning method for the iterative solution of linear systems that arise in the… (more)

▼

This project is concerned with the development and implementation of a novel preconditioning method for the iterative solution of linear systems that arise in the finite element discretisation of the incompressible Navier-Stokes equations with weakly imposed boundary conditions. In this context we studied an augmented approach where the Schur complement associated with the momentum block of the Navier-Stokes equations has special sparse structure. We follow the standard inf-sup stable method of discretising the Navier-Stokes equations by the Taylor-Hood elements with the Lagrange multiplier constraints discretised using the same order approximation on matching grids. The resulting system of nonlinear equations is solved iteratively by Newton's method. The spectrum of the linearised Oseen's problem, preconditioned by the exact augmentation preconditioner was analysed. Then we developed inexact versions of the preconditioner aimed at achieving optimal scaling of the algorithm in terms of computational resources and wall-clock times. The experimental evaluation of the methodology involve a number of benchmark problems in two and three spatial dimensions. The obtained results demonstrate efficiency, robustness and almost optimal scaling of the solution algorithm with respect to the discrete problem size.We used OOMPH-LIB as a testbed for our experiments. The preconditioning strategies were implemented using OOMPH-LIB's Parallel Block Preconditioning Framework. The initial version of the software was significantly upgraded during the course of this project with newly implemented functionalities to facilitate the rapid development of sophisticated hierarchical design of parallel block preconditioners. Parallel performance analysis of the newly introduced functionalities demonstrate negligible overhead in terms of wall-clock time and the framework demonstrate good weak and strong parallel scaling.

This project is concerned with the development and implementation of a novel preconditioning method for the iterative solution of linear systems that arise in the finite element discretisation of the incompressible Navier-Stokes equations with weakly imposed boundary conditions. In this context we studied an augmented approach where the Schur complement associated with the momentum block of the Navier-Stokes equations has special sparse structure. We follow the standard inf-sup stable method of discretising the Navier-Stokes equations by the Taylor-Hood elements with the Lagrange multiplier constraints discretised using the same order approximation on matching grids. The resulting system of nonlinear equations is solved iteratively by Newton's method. The spectrum of the linearised Oseen's problem, preconditioned by the exact augmentation preconditioner was analysed. Then we developed inexact versions of the preconditioner aimed at achieving optimal scaling of the algorithm in terms of computational resources and wall-clock times. The experimental evaluation of the methodology involve a number of benchmark problems in two and…

Advisors/Committee Members: Mihajlovic, Milan.

Subjects/Keywords: Navier-Stokes; Linear Solver; Iterative Linear Solver; Preconditioner; Boundary Conditions; Parallel Programming; Block Preconditioner; OOMPH-LIB; C++

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APA (6^th Edition):

White, R. (2016). Parallel Block Preconditioning of the Incompressible Navier-Stokes Equations with Weakly Imposed Boundary Conditions. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:305538

Chicago Manual of Style (16^th Edition):

White, Raymon. “Parallel Block Preconditioning of the Incompressible Navier-Stokes Equations with Weakly Imposed Boundary Conditions.” 2016. Doctoral Dissertation, University of Manchester. Accessed April 15, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:305538.

MLA Handbook (7^th Edition):

White, Raymon. “Parallel Block Preconditioning of the Incompressible Navier-Stokes Equations with Weakly Imposed Boundary Conditions.” 2016. Web. 15 Apr 2021.

Vancouver:

White R. Parallel Block Preconditioning of the Incompressible Navier-Stokes Equations with Weakly Imposed Boundary Conditions. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2021 Apr 15]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:305538.

Council of Science Editors:

White R. Parallel Block Preconditioning of the Incompressible Navier-Stokes Equations with Weakly Imposed Boundary Conditions. [Doctoral Dissertation]. University of Manchester; 2016. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:305538

9. Van Zwieten, J.S.B. (author). Efficient solution methods for the incompressible Stokes problem.

Degree: 2012, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:dd7b9002-03c9-4976-8bf8-6c91885608ef

Applied mathematics

Electrical Engineering, Mathematics and Computer Science

Advisors/Committee Members: Van Gijzen, M.B. (mentor), Van Male, J. (mentor).

Subjects/Keywords: stokes; linear solver; preconditioner

…transform suitable for shear periodic boundaries is described and a preconditioner is defined for… …preconditioner are extended to three dimensional problems in Chapter 6. All solution methods defined in… …Fourier based preconditioner, as described in Chapters 5 and 6, is not found in literature by… …originating from a matrix splitting A = M − N can be used as a preconditioner. As such, the basic… …the most simple preconditioner is diagonal scaling, M = diag(A). The computational…

1 more image…

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APA (6^th Edition):

Van Zwieten, J. S. B. (. (2012). Efficient solution methods for the incompressible Stokes problem. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:dd7b9002-03c9-4976-8bf8-6c91885608ef

Chicago Manual of Style (16^th Edition):

Van Zwieten, J S B (author). “Efficient solution methods for the incompressible Stokes problem.” 2012. Masters Thesis, Delft University of Technology. Accessed April 15, 2021. http://resolver.tudelft.nl/uuid:dd7b9002-03c9-4976-8bf8-6c91885608ef.

MLA Handbook (7^th Edition):

Van Zwieten, J S B (author). “Efficient solution methods for the incompressible Stokes problem.” 2012. Web. 15 Apr 2021.

Vancouver:

Van Zwieten JSB(. Efficient solution methods for the incompressible Stokes problem. [Internet] [Masters thesis]. Delft University of Technology; 2012. [cited 2021 Apr 15]. Available from: http://resolver.tudelft.nl/uuid:dd7b9002-03c9-4976-8bf8-6c91885608ef.

Council of Science Editors:

Van Zwieten JSB(. Efficient solution methods for the incompressible Stokes problem. [Masters Thesis]. Delft University of Technology; 2012. Available from: http://resolver.tudelft.nl/uuid:dd7b9002-03c9-4976-8bf8-6c91885608ef

10. ZHAI XIAOJUN. Two problems in convex conic optimization.

Degree: 2007, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/13388

Subjects/Keywords: SEBB; QSDP; smooth; preconditioner

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APA (6^th Edition):

XIAOJUN, Z. (2007). Two problems in convex conic optimization. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/13388

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):

XIAOJUN, ZHAI. “Two problems in convex conic optimization.” 2007. Thesis, National University of Singapore. Accessed April 15, 2021. http://scholarbank.nus.edu.sg/handle/10635/13388.

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

MLA Handbook (7^th Edition):

XIAOJUN, ZHAI. “Two problems in convex conic optimization.” 2007. Web. 15 Apr 2021.

Vancouver:

XIAOJUN Z. Two problems in convex conic optimization. [Internet] [Thesis]. National University of Singapore; 2007. [cited 2021 Apr 15]. Available from: http://scholarbank.nus.edu.sg/handle/10635/13388.

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

Council of Science Editors:

XIAOJUN Z. Two problems in convex conic optimization. [Thesis]. National University of Singapore; 2007. Available from: http://scholarbank.nus.edu.sg/handle/10635/13388

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

Georgia Tech

11. Jian, Yong-Dian. Support-theoretic subgraph preconditioners for large-scale SLAM and structure from motion.

Degree: PhD, Computer Science, 2014, Georgia Tech

URL: http://hdl.handle.net/1853/52272

► Simultaneous localization and mapping (SLAM) and Structure from Motion (SfM) are important problems in robotics and computer vision. One of the challenges is to solve… (more)

▼ Simultaneous localization and mapping (SLAM) and Structure from Motion (SfM) are important problems in robotics and computer vision. One of the challenges is to solve a large-scale optimization problem associated with all of the robot poses, camera parameters, landmarks and measurements. Yet neither of the two reigning paradigms, direct and iterative methods, scales well to very large and complex problems. Recently, the subgraph-preconditioned conjugate gradient method has been proposed to combine the advantages of direct and iterative methods. However, how to find a good subgraph is still an open problem. The goal of this dissertation is to address the following two questions: (1) What are good subgraph preconditioners for SLAM and SfM? (2) How to find them? To this end, I introduce support theory and support graph theory to evaluate and design subgraph preconditioners for SLAM and SfM. More specifically, I make the following contributions: First, I develop graphical and probabilistic interpretations of support theory and used them to visualize the quality of subgraph preconditioners. Second, I derive a novel support-theoretic metric for the quality of spanning tree preconditioners and design an MCMC-based algorithm to find high-quality subgraph preconditioners. I further improve the efficiency of finding good subgraph preconditioners by using heuristics and domain knowledge available in the problems. Our results show that the support-theoretic subgraph preconditioners significantly improve the efficiency of solving large SLAM problems. Third, I propose a novel Hessian factor graph representation, and use it to develop a new class of preconditioners, generalized subgraph preconditioners, that combine the advantages of subgraph preconditioners and Hessian-based preconditioners. I apply them to solve large SfM problems and obtain promising results. Fourth, I develop the incremental subgraph-preconditioned conjugate gradient method for large-scale online SLAM problems. The main idea is to combine the advantages of two state-of-the-art methods, incremental smoothing and mapping, and the subgraph-preconditioned conjugate gradient method. I also show that the new method is efficient, optimal and consistent. To sum up, preconditioning can significantly improve the efficiency of solving large-scale SLAM and SfM problems. While existing preconditioning techniques do not utilize the problem structure and have no performance guarantee, I take the first step toward a more general setting and have promising results. Advisors/Committee Members: Dellaert, Frank (advisor), Chow, Edmond (committee member), Rehg, James M. (committee member), Snavely, Noah (committee member), Tetali, Prasad (committee member).

Subjects/Keywords: SLAM; Structure from motion; Preconditioning; Subgraph preconditioner; Support theory

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APA (6^th Edition):

Jian, Y. (2014). Support-theoretic subgraph preconditioners for large-scale SLAM and structure from motion. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/52272

Chicago Manual of Style (16^th Edition):

Jian, Yong-Dian. “Support-theoretic subgraph preconditioners for large-scale SLAM and structure from motion.” 2014. Doctoral Dissertation, Georgia Tech. Accessed April 15, 2021. http://hdl.handle.net/1853/52272.

MLA Handbook (7^th Edition):

Jian, Yong-Dian. “Support-theoretic subgraph preconditioners for large-scale SLAM and structure from motion.” 2014. Web. 15 Apr 2021.

Vancouver:

Jian Y. Support-theoretic subgraph preconditioners for large-scale SLAM and structure from motion. [Internet] [Doctoral dissertation]. Georgia Tech; 2014. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/1853/52272.

Council of Science Editors:

Jian Y. Support-theoretic subgraph preconditioners for large-scale SLAM and structure from motion. [Doctoral Dissertation]. Georgia Tech; 2014. Available from: http://hdl.handle.net/1853/52272

Louisiana State University

12. Gu, Shiyuan. C0 Interior Penalty Methods for Cahn-Hilliard Equations.

Degree: PhD, Applied Mathematics, 2012, Louisiana State University

URL: etd-06052012-123115 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1744

► In this work we study C0 interior penalty methods for Cahn-Hilliard equations. In Chapter 1 we introduce Cahn-Hilliard equations and the time discretization that leads… (more)

Subjects/Keywords: preconditioner; medius analysis; adaptive mesh refinement; discontinuous Galerkin method

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

APA (6^th Edition):

Gu, S. (2012). C0 Interior Penalty Methods for Cahn-Hilliard Equations. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-06052012-123115 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1744

Chicago Manual of Style (16^th Edition):

Gu, Shiyuan. “C0 Interior Penalty Methods for Cahn-Hilliard Equations.” 2012. Doctoral Dissertation, Louisiana State University. Accessed April 15, 2021. etd-06052012-123115 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1744.

MLA Handbook (7^th Edition):

Gu, Shiyuan. “C0 Interior Penalty Methods for Cahn-Hilliard Equations.” 2012. Web. 15 Apr 2021.

Vancouver:

Gu S. C0 Interior Penalty Methods for Cahn-Hilliard Equations. [Internet] [Doctoral dissertation]. Louisiana State University; 2012. [cited 2021 Apr 15]. Available from: etd-06052012-123115 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1744.

Council of Science Editors:

Gu S. C0 Interior Penalty Methods for Cahn-Hilliard Equations. [Doctoral Dissertation]. Louisiana State University; 2012. Available from: etd-06052012-123115 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1744

University of Manchester

13. Perez Sansalvador, Julio Cesar. Parallel Unstructured Mesh Adaptation and Applications.

Degree: 2016, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303572

► In this thesis we develop 2D parallel unstructured mesh adaptationmethods for the solution of partial differential equations (PDEs) bythe finite element method (FEM). Additionally, we… (more)

▼ In this thesis we develop 2D parallel unstructured mesh adaptationmethods for the solution of partial differential equations (PDEs) bythe finite element method (FEM). Additionally, we develop a novelblock preconditioner for the iterative solution of the linear systemsarising from the finite element discretisation of the Föppl-von Kàrmànequations.Two of the problems arising in the numerical solution of PDEs by FEMare the memory constraints that limit the solution of large problems,and the inefficiency of solving the associated linear systems bydirect or iterative solvers.We initially focus on mesh adaptation, which is a memory demandingtask of the FEM. The size of the problem increases by adding moreelements and nodes to the mesh during mesh refinement. In problemsinvolving a large number of elements, the problem size is limited bythe memory available on a single processor.In order to be able to work with large problems, we use a domaindecomposition approach to distribute the problem over multipleprocessors. One of the main objectives of this thesis is thedevelopment of 2D parallel unstructured mesh adaptation methods forthe solution of PDEs by the FEM in a variety of problems; includingdomains with curved boundaries, holes and internal boundaries. Ournewly developed methods are implemented in the software libraryoomph-lib, an open-source object oriented multi-physicssoftware library implementing the FEM. We validate and demonstratetheir utility in a set of increasingly complex problems ranging fromscalar PDEs to fully coupled multi-physics problems.Having implemented and validated the infrastructure which facilitatesthe finite-element-based discretisation of PDEs in a distributedenvironment, we shift our focus to the second problem concerning thisthesis and one of the major challenges in the computational solutionof PDEs: the solution of the large linear systems arising from theirdiscretisation.For sufficiently large problems, the solution of their associatedlinear system by direct solvers becomes impossible or inefficient,typically because of memory and time constraints. We therefore focuson preconditioned Krylov subspace methods whose efficiency dependscrucially on the provision of a good preconditioner. Thesepreconditioners are invariably problem dependent. We illustrate theirapplication and development in the solution of two elasticity problemswhich give rise to relatively large problems.First we consider the solution of a linear elasticity problem andcompute the stress distribution near a crack tip where strong localmesh refinement is required. We then consider the deformation of thinplates which are described by the nonlinear Föppl-von Kàrmànequations. A key contribution of this work is the development of anovel block preconditioner for the iterative solution of theseequations, we present the development of the preconditioner anddemonstrate its practical performance. Advisors/Committee Members: HAZEL, ANDREW A, Heil, Matthias, Hazel, Andrew.

Subjects/Keywords: Parallel unstructured mesh adaptation; Föppl-von Kàrmàn; Preconditioner; Elasticity; oomph-lib

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

APA (6^th Edition):

Perez Sansalvador, J. C. (2016). Parallel Unstructured Mesh Adaptation and Applications. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303572

Chicago Manual of Style (16^th Edition):

Perez Sansalvador, Julio Cesar. “Parallel Unstructured Mesh Adaptation and Applications.” 2016. Doctoral Dissertation, University of Manchester. Accessed April 15, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303572.

MLA Handbook (7^th Edition):

Perez Sansalvador, Julio Cesar. “Parallel Unstructured Mesh Adaptation and Applications.” 2016. Web. 15 Apr 2021.

Vancouver:

Perez Sansalvador JC. Parallel Unstructured Mesh Adaptation and Applications. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2021 Apr 15]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303572.

Council of Science Editors:

Perez Sansalvador JC. Parallel Unstructured Mesh Adaptation and Applications. [Doctoral Dissertation]. University of Manchester; 2016. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303572

University of Sydney

14. Djanali, Vivien Suphandani. The Fractional Step Navier–Stokes Solver: Preconditioning and Application to Conjugate Natural Convection Boundary Layers .

Degree: 2013, University of Sydney

URL: http://hdl.handle.net/2123/9472

► Viscous, incompressible flow is governed by the Navier–Stokes equations. The simulation of this flow is difficult to solve due to the coupling between the pressure… (more)

Subjects/Keywords: Navier-Stokes solver; preconditioner; natural convection conjugate boundary layer

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APA (6^th Edition):

Djanali, V. S. (2013). The Fractional Step Navier–Stokes Solver: Preconditioning and Application to Conjugate Natural Convection Boundary Layers . (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/9472

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):

Djanali, Vivien Suphandani. “The Fractional Step Navier–Stokes Solver: Preconditioning and Application to Conjugate Natural Convection Boundary Layers .” 2013. Thesis, University of Sydney. Accessed April 15, 2021. http://hdl.handle.net/2123/9472.

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

MLA Handbook (7^th Edition):

Djanali, Vivien Suphandani. “The Fractional Step Navier–Stokes Solver: Preconditioning and Application to Conjugate Natural Convection Boundary Layers .” 2013. Web. 15 Apr 2021.

Vancouver:

Djanali VS. The Fractional Step Navier–Stokes Solver: Preconditioning and Application to Conjugate Natural Convection Boundary Layers . [Internet] [Thesis]. University of Sydney; 2013. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/2123/9472.

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

Council of Science Editors:

Djanali VS. The Fractional Step Navier–Stokes Solver: Preconditioning and Application to Conjugate Natural Convection Boundary Layers . [Thesis]. University of Sydney; 2013. Available from: http://hdl.handle.net/2123/9472

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

Texas A&M University

15. Leal Chapa, Jesus Jaime. Proper Orthogonal Decomposition for Pressure Preconditioning for the GMRES Algorithm.

Degree: MS, Petroleum Engineering, 2016, Texas A&M University

URL: http://hdl.handle.net/1969.1/158657

► The linear solver in a typical reservoir simulator consumes around 60 to 70 % of the total simulation time. To speed up the solution of… (more)

Subjects/Keywords: pod; GMRES; preconditioner; model reduction; proper orthogonal decomposition; reservoir simulation; linear solver

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

APA (6^th Edition):

Leal Chapa, J. J. (2016). Proper Orthogonal Decomposition for Pressure Preconditioning for the GMRES Algorithm. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/158657

Chicago Manual of Style (16^th Edition):

Leal Chapa, Jesus Jaime. “Proper Orthogonal Decomposition for Pressure Preconditioning for the GMRES Algorithm.” 2016. Masters Thesis, Texas A&M University. Accessed April 15, 2021. http://hdl.handle.net/1969.1/158657.

MLA Handbook (7^th Edition):

Leal Chapa, Jesus Jaime. “Proper Orthogonal Decomposition for Pressure Preconditioning for the GMRES Algorithm.” 2016. Web. 15 Apr 2021.

Vancouver:

Leal Chapa JJ. Proper Orthogonal Decomposition for Pressure Preconditioning for the GMRES Algorithm. [Internet] [Masters thesis]. Texas A&M University; 2016. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/1969.1/158657.

Council of Science Editors:

Leal Chapa JJ. Proper Orthogonal Decomposition for Pressure Preconditioning for the GMRES Algorithm. [Masters Thesis]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/158657

University of Manchester

16. Perez Sansalvador, Julio. Parallel unstructured mesh adaptation and applications.

Degree: PhD, 2016, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/parallel-unstructured-mesh-adaptation-and-applications(26248d4d-48a6-4101-a687-004218e39cb4).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727916

► In this thesis we develop 2D parallel unstructured mesh adaptation methods for the solution of partial differential equations (PDEs) by the finite element method (FEM).… (more)

▼ In this thesis we develop 2D parallel unstructured mesh adaptation methods for the solution of partial differential equations (PDEs) by the finite element method (FEM). Additionally, we develop a novel block preconditioner for the iterative solution of the linear systems arising from the finite element discretisation of the Föppl-von Kàrmàn equations. Two of the problems arising in the numerical solution of PDEs by FEM are the memory constraints that limit the solution of large problems, and the inefficiency of solving the associated linear systems by direct or iterative solvers. We initially focus on mesh adaptation, which is a memory demanding task of the FEM. The size of the problem increases by adding more elements and nodes to the mesh during mesh refinement. In problems involving a large number of elements, the problem size is limited by the memory available on a single processor. In order to be able to work with large problems, we use a domain decomposition approach to distribute the problem over multiple processors. One of the main objectives of this thesis is the development of 2D parallel unstructured mesh adaptation methods for the solution of PDEs by the FEM in a variety of problems; including domains with curved boundaries, holes and internal boundaries. Our newly developed methods are implemented in the software library oomph-lib, an open-source object oriented multi-physics software library implementing the FEM. We validate and demonstrate their utility in a set of increasingly complex problems ranging from scalar PDEs to fully coupled multi-physics problems. Having implemented and validated the infrastructure which facilitates the finite-element-based discretisation of PDEs in a distributed environment, we shift our focus to the second problem concerning this thesis and one of the major challenges in the computational solution of PDEs: the solution of the large linear systems arising from their discretisation. For sufficiently large problems, the solution of their associated linear system by direct solvers becomes impossible or inefficient, typically because of memory and time constraints. We therefore focus on preconditioned Krylov subspace methods whose efficiency depends crucially on the provision of a good preconditioner. These preconditioners are invariably problem dependent. We illustrate their application and development in the solution of two elasticity problems which give rise to relatively large problems. First we consider the solution of a linear elasticity problem and compute the stress distribution near a crack tip where strong local mesh refinement is required. We then consider the deformation of thin plates which are described by the nonlinear Föppl-von Kàrmàn equations. A key contribution of this work is the development of a novel block preconditioner for the iterative solution of these equations, we present the development of the preconditioner and demonstrate its practical performance.

Subjects/Keywords: 515; Elasticity; oomph-lib; Föppl-von Kàrmàn; Parallel unstructured mesh adaptation; Preconditioner

Record Details Similar Records Cite « Share

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

APA (6^th Edition):

Perez Sansalvador, J. (2016). Parallel unstructured mesh adaptation and applications. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/parallel-unstructured-mesh-adaptation-and-applications(26248d4d-48a6-4101-a687-004218e39cb4).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727916

Chicago Manual of Style (16^th Edition):

Perez Sansalvador, Julio. “Parallel unstructured mesh adaptation and applications.” 2016. Doctoral Dissertation, University of Manchester. Accessed April 15, 2021. https://www.research.manchester.ac.uk/portal/en/theses/parallel-unstructured-mesh-adaptation-and-applications(26248d4d-48a6-4101-a687-004218e39cb4).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727916.

MLA Handbook (7^th Edition):

Perez Sansalvador, Julio. “Parallel unstructured mesh adaptation and applications.” 2016. Web. 15 Apr 2021.

Vancouver:

Perez Sansalvador J. Parallel unstructured mesh adaptation and applications. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2021 Apr 15]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/parallel-unstructured-mesh-adaptation-and-applications(26248d4d-48a6-4101-a687-004218e39cb4).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727916.

Council of Science Editors:

Perez Sansalvador J. Parallel unstructured mesh adaptation and applications. [Doctoral Dissertation]. University of Manchester; 2016. Available from: https://www.research.manchester.ac.uk/portal/en/theses/parallel-unstructured-mesh-adaptation-and-applications(26248d4d-48a6-4101-a687-004218e39cb4).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727916

Delft University of Technology

17. Buwalda, Floris (author). Suitability of Shallow Water Solving Methods for GPU Acceleration.

Degree: 2020, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:bec8d3b2-f8d0-4cd1-8178-d5abaa2a4de9

►

In the past 15 years the field of general purpose computing on graphics processing units, or GPUs, has become well developed and the practice is… (more)

▼

In the past 15 years the field of general purpose computing on graphics processing units, or GPUs, has become well developed and the practice is becoming more mainstream. Computational demands of simulation software are continuously increasing. As such for many applications traditionally computed on the central processing unit the question arises of whether moving to GPU computing is a possible cost effective way of meeting these demands. The fundamental nature of GPU architecture that makes it so cost effective at doing bulk computation also poses restrictions on which applications are suitable for it. The shallow water equations are a simplified form of the Navier-Stokes equations and describe water levels and flow currents in suitably shallow water such as rivers, estuaries and the North sea. The main research goal of this thesis project was to determine whether the shallow water equations are suitable for implementation on a GPU. Two options exist, the equations may be solved with either an explicit or implicit time integration method. First, a literature study was conducted to familiarize with the tools required to build explicit and implicit shallow water models on a GPU. Then both an explicit and implicit shallow water solver were developed first in the MATLAB programming language and later in CUDA C++ on both CPU and GPU. The main findings are that both explicit and implicit methods are well suited for GPU implementation. Both methods proved to be compatible with a wetting and drying mechanism of numerical cells. The Cuda C++ implementation was in the order of 10 times as fast as a MATLAB implementation for both CPU and GPU. For the benchmark cases tested, the Cuda C++ GPU implementation was in the order of 50 times faster than the equivalent multithreaded CPU implementation. The implicit implementation was benchmarked using the conjugate gradient method to solve the linear system. Various preconditioners were tested and a Repeated Red Black preconditioner was found to be the most effective. The computation time of the RRB preconditioned implicit method was compared with the explicit method and it was found that the two methods reached parity in computation time when the implicit time step was taken roughly 50 times as large as the explicit time step. For implicit time steps smaller than that the explicit method was faster and when the implicit time step was larger the implicit method was faster. For the benchmark cases tested, the implicit method using a time step 50 times larger than the explicit method was found to be less accurate and less stable than the explicit method. The conclusion is that for cases similar to the benchmark cases an explicit method is the fastest, most stable and most accurate method and thus the preferred choice.

Applied Mathematics

Advisors/Committee Members: Vuik, Kees (mentor), de Goede, Erik (graduation committee), Pronk, Maarten (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: GPU; Shallow Water Equations; Time integration; Structured grid; Conjugate Gradient; CUDA; Preconditioner

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

APA (6^th Edition):

Buwalda, F. (. (2020). Suitability of Shallow Water Solving Methods for GPU Acceleration. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:bec8d3b2-f8d0-4cd1-8178-d5abaa2a4de9

Chicago Manual of Style (16^th Edition):

Buwalda, Floris (author). “Suitability of Shallow Water Solving Methods for GPU Acceleration.” 2020. Masters Thesis, Delft University of Technology. Accessed April 15, 2021. http://resolver.tudelft.nl/uuid:bec8d3b2-f8d0-4cd1-8178-d5abaa2a4de9.

MLA Handbook (7^th Edition):

Buwalda, Floris (author). “Suitability of Shallow Water Solving Methods for GPU Acceleration.” 2020. Web. 15 Apr 2021.

Vancouver:

Buwalda F(. Suitability of Shallow Water Solving Methods for GPU Acceleration. [Internet] [Masters thesis]. Delft University of Technology; 2020. [cited 2021 Apr 15]. Available from: http://resolver.tudelft.nl/uuid:bec8d3b2-f8d0-4cd1-8178-d5abaa2a4de9.

Council of Science Editors:

Buwalda F(. Suitability of Shallow Water Solving Methods for GPU Acceleration. [Masters Thesis]. Delft University of Technology; 2020. Available from: http://resolver.tudelft.nl/uuid:bec8d3b2-f8d0-4cd1-8178-d5abaa2a4de9

Michigan Technological University

18. Zhao, Xueqian. FAST VERY-LARGE-SCALE INTEGRATED (VLSI) CIRCUITS SIMULATIONS.

Degree: PhD, Department of Electrical and Computer Engineering, 2018, Michigan Technological University

URL: https://digitalcommons.mtu.edu/etdr/637

► To evaluate and verify the functional correction and reliability of circuit designs, circuit components (e.g. resistors, capacitors, etc) need to be accurately modeled (e.g.… (more)

▼ To evaluate and verify the functional correction and reliability of circuit designs, circuit components (e.g. resistors, capacitors, etc) need to be accurately modeled (e.g. parasitic extraction) and circuit performance requires precise analysis (e.g. simulation and verification). As the technology scaling of nowadays integrated circuits enters nano-scale regime, the traditional flow of circuit designs becomes increasingly challenging due to the rapid growth of circuit complexity brought by more than billions on-chip components. To this end, during the past decades, endless effort has been made to increase the design efficiency via various directions that include but not limited to exploration of advanced algorithms, leveraging the benefits of multi-core/many-core heterogeneous computation platforms. For full chip parasitic extraction, we propose GPU-friendly data structures and single-instruction-multiple-data (SIMD) parallel algorithm flows to facilitate the FMM-based 3-D capacitance extraction on GPU. Effective GPU performance modeling methods are also proposed to properly balance the workload of each critical kernel in our FMMGpu implementation, by taking advantage of the GPU's concurrent kernel execution technique. Our experimental results show that FMMGpu brings 22X to 30X speedups in capacitance extractions for various test cases. For circuit simulations, based on recent graph sparsification research, we propose a circuit-oriented general-purpose support-circuit preconditioning (GPSCP) approach to improve the matrix solving time and reduce the memory consumption during SPICE-accurate integrated circuit simulations. Additionally, a performance model-guided graph sparsification approach is proposed to facilitate automatically building a near-optimal preconditioner. Our experimental results for a variety of large-scale integrated circuit designs show that the proposed technique can achieve up to 18X runtime speedups and 7X memory reduction in DC and transient Simulations. Besides accelerating the analysis by effective preconditioners, we also explore a scalable power grid reduction method for reducing large-scale flip-chip power grids based on recent spectral graph sparsification techniques. In our work, Schur complement and spectral graph sparsification methods are combined to reduce the original large power grid into a much smaller grid while keeping affordable grid density for fast analysis. Extensive experimental results show that our method can scale linearly with power grid sizes and efficiently reduce industrial power grids sizes by 20X without loss of much accuracy in both DC and transient analysis. Advisors/Committee Members: Zhuo Feng.

Subjects/Keywords: VLSI; SIMULATION; PRECONDITIONER; GPU; Electrical and Electronics; VLSI and Circuits, Embedded and Hardware Systems

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

APA (6^th Edition):

Zhao, X. (2018). FAST VERY-LARGE-SCALE INTEGRATED (VLSI) CIRCUITS SIMULATIONS. (Doctoral Dissertation). Michigan Technological University. Retrieved from https://digitalcommons.mtu.edu/etdr/637

Chicago Manual of Style (16^th Edition):

Zhao, Xueqian. “FAST VERY-LARGE-SCALE INTEGRATED (VLSI) CIRCUITS SIMULATIONS.” 2018. Doctoral Dissertation, Michigan Technological University. Accessed April 15, 2021. https://digitalcommons.mtu.edu/etdr/637.

MLA Handbook (7^th Edition):

Zhao, Xueqian. “FAST VERY-LARGE-SCALE INTEGRATED (VLSI) CIRCUITS SIMULATIONS.” 2018. Web. 15 Apr 2021.

Vancouver:

Zhao X. FAST VERY-LARGE-SCALE INTEGRATED (VLSI) CIRCUITS SIMULATIONS. [Internet] [Doctoral dissertation]. Michigan Technological University; 2018. [cited 2021 Apr 15]. Available from: https://digitalcommons.mtu.edu/etdr/637.

Council of Science Editors:

Zhao X. FAST VERY-LARGE-SCALE INTEGRATED (VLSI) CIRCUITS SIMULATIONS. [Doctoral Dissertation]. Michigan Technological University; 2018. Available from: https://digitalcommons.mtu.edu/etdr/637

Rice University

19. Wang, Yingpei. On the approximation of the Dirichlet to Neumann map for high contrast two phase composites and its applications to domain decomposition methods.

Degree: PhD, Engineering, 2014, Rice University

URL: http://hdl.handle.net/1911/88418

► An asymptotic approximation of the Dirichlet to Neumann (DtN) map of high contrast composite media with perfectly conducting inclusions that are close to touching is… (more)

Subjects/Keywords: Asymptotic approximation; high contrast; Dirichlet to Neumann Map; domain decomposition methods; preconditioner

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

APA (6^th Edition):

Wang, Y. (2014). On the approximation of the Dirichlet to Neumann map for high contrast two phase composites and its applications to domain decomposition methods. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/88418

Chicago Manual of Style (16^th Edition):

Wang, Yingpei. “On the approximation of the Dirichlet to Neumann map for high contrast two phase composites and its applications to domain decomposition methods.” 2014. Doctoral Dissertation, Rice University. Accessed April 15, 2021. http://hdl.handle.net/1911/88418.

MLA Handbook (7^th Edition):

Wang, Yingpei. “On the approximation of the Dirichlet to Neumann map for high contrast two phase composites and its applications to domain decomposition methods.” 2014. Web. 15 Apr 2021.

Vancouver:

Wang Y. On the approximation of the Dirichlet to Neumann map for high contrast two phase composites and its applications to domain decomposition methods. [Internet] [Doctoral dissertation]. Rice University; 2014. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/1911/88418.

Council of Science Editors:

Wang Y. On the approximation of the Dirichlet to Neumann map for high contrast two phase composites and its applications to domain decomposition methods. [Doctoral Dissertation]. Rice University; 2014. Available from: http://hdl.handle.net/1911/88418

Penn State University

20. Zhu, Yunrong. ROBUST PRECONDITIONERS FOR H(grad), H(curl) AND H(div) SYSTEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS.

Degree: 2008, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/8775

► This dissertation is devoted to practical design and theoretical analysis of efficient and robust preconditioners for solving algebraic systems arising from the approximation of partial… (more)

▼ This dissertation is devoted to practical design and theoretical analysis of efficient and robust preconditioners for solving algebraic systems arising from the approximation of partial differential equations, with special emphasis on the problems with strongly discontinuous coefficients. The problems considered here include the standard second order elliptic equations (H(grad) or H¹ equations), as well as the second order elliptic systems given in terms of curl and divergence operators (H(curl) and H(div) systems). In regard to the H¹ equations with jump coefficients, we study both the multilevel and domain decomposition preconditioners. We analyze the eigenvalue distribution of the preconditioned systems, and prove that only a small number of eigenvalues may deteriorate with respect to coefficients and mesh size. We show that the other eigenvalues are bounded uniformly with respect to the coefficients of the PDE and bounded poly-logarithmically with respect to mesh size. As a result, the asymptotic convergence rate of the PCG algorithms is uniform with respect to the coefficients, and nearly uniform (up to a logarithmic factor) with respect to the mesh size. Various numerical experiments justify the theoretical results. For H(curl) and H(div) systems, we give a comprehensive analysis of auxiliary space preconditioners, which rely on regular decompositions. Through such constructions, these preconditioners reduce H(curl) and H(div) systems to the solution of several H(grad) equations, which are amenable by standard algebraic multigrid (AMG) techniques. We also develop a preconditioner for H(curl) systems with jump coefficients. We show that the condition number of the preconditioned system is uniformly bounded with respect to coefficients and mesh size. Another class of preconditioners that we propose are the compatible AMG preconditioners for H(curl) and H(div) systems. This approach makes use of a compatible discretization framework. We reformulate the discrete systems into equivalent 2-by-2 block systems based on discrete Hodge decompositions on co-chains, and then construct the AMG preconditioners for the 2-by-2 block systems. As an important application, we present the augmented Lagrangian method for solving mixed formulations of elliptic boundary value problems, which reduces a saddle point problem to a nearly singular H(div) system. Advisors/Committee Members: Jinchao Xu, Committee Chair/Co-Chair, Victor Nistor, Committee Member, Francesco Costanzo, Committee Member, Ludmil Tomov Zikatanov, Committee Member, Anna L Mazzucato, Committee Member.

Subjects/Keywords: Jump Coefficients; Multigrid; BPX preconditioner; Domain Decomposition; Condition Number

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

APA (6^th Edition):

Zhu, Y. (2008). ROBUST PRECONDITIONERS FOR H(grad), H(curl) AND H(div) SYSTEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/8775

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):

Zhu, Yunrong. “ROBUST PRECONDITIONERS FOR H(grad), H(curl) AND H(div) SYSTEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS.” 2008. Thesis, Penn State University. Accessed April 15, 2021. https://submit-etda.libraries.psu.edu/catalog/8775.

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

MLA Handbook (7^th Edition):

Zhu, Yunrong. “ROBUST PRECONDITIONERS FOR H(grad), H(curl) AND H(div) SYSTEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS.” 2008. Web. 15 Apr 2021.

Vancouver:

Zhu Y. ROBUST PRECONDITIONERS FOR H(grad), H(curl) AND H(div) SYSTEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS. [Internet] [Thesis]. Penn State University; 2008. [cited 2021 Apr 15]. Available from: https://submit-etda.libraries.psu.edu/catalog/8775.

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

Council of Science Editors:

Zhu Y. ROBUST PRECONDITIONERS FOR H(grad), H(curl) AND H(div) SYSTEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS. [Thesis]. Penn State University; 2008. Available from: https://submit-etda.libraries.psu.edu/catalog/8775

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

Texas A&M University

21. Wei, Jia. Reduced Order Model and Uncertainty Quantification for Stochastic Porous Media Flows.

Degree: PhD, Mathematics, 2012, Texas A&M University

URL: http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11598

► In this dissertation, we focus on the uncertainty quantification problems where the goal is to sample the porous media properties given integrated responses. We first… (more)

Subjects/Keywords: uncertainty quantification; regularity of posterior; ensemble-level; preconditioner; analysis of variance; mixed multiscale finite element method; multi-stage SAMC

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

APA (6^th Edition):

Wei, J. (2012). Reduced Order Model and Uncertainty Quantification for Stochastic Porous Media Flows. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11598

Chicago Manual of Style (16^th Edition):

Wei, Jia. “Reduced Order Model and Uncertainty Quantification for Stochastic Porous Media Flows.” 2012. Doctoral Dissertation, Texas A&M University. Accessed April 15, 2021. http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11598.

MLA Handbook (7^th Edition):

Wei, Jia. “Reduced Order Model and Uncertainty Quantification for Stochastic Porous Media Flows.” 2012. Web. 15 Apr 2021.

Vancouver:

Wei J. Reduced Order Model and Uncertainty Quantification for Stochastic Porous Media Flows. [Internet] [Doctoral dissertation]. Texas A&M University; 2012. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11598.

Council of Science Editors:

Wei J. Reduced Order Model and Uncertainty Quantification for Stochastic Porous Media Flows. [Doctoral Dissertation]. Texas A&M University; 2012. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11598

University of Waterloo

22. Bridson, Robert. Multi-Resolution Approximate Inverses.

Degree: 1999, University of Waterloo

URL: http://hdl.handle.net/10012/1167

► This thesis presents a new preconditioner for elliptic PDE problems on unstructured meshes. Using ideas from second generation wavelets, a multi-resolution basis is constructed to… (more)

Subjects/Keywords: Mathematics; numerical; linear; preconditioner; elliptic; PDE; wavelets

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

APA (6^th Edition):

Bridson, R. (1999). Multi-Resolution Approximate Inverses. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/1167

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):

Bridson, Robert. “Multi-Resolution Approximate Inverses.” 1999. Thesis, University of Waterloo. Accessed April 15, 2021. http://hdl.handle.net/10012/1167.

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

MLA Handbook (7^th Edition):

Bridson, Robert. “Multi-Resolution Approximate Inverses.” 1999. Web. 15 Apr 2021.

Vancouver:

Bridson R. Multi-Resolution Approximate Inverses. [Internet] [Thesis]. University of Waterloo; 1999. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/10012/1167.

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

Council of Science Editors:

Bridson R. Multi-Resolution Approximate Inverses. [Thesis]. University of Waterloo; 1999. Available from: http://hdl.handle.net/10012/1167

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

23. Negrello, Camille. Méthodes fortement parallèles pour la simulation numérique en mécanique non linéaire des structures : Highly parallel methods for numerical simulation in nonlinear structural mechanics.

Degree: Docteur es, Mécanique des solides, 2017, Université Paris-Saclay (ComUE)

URL: http://www.theses.fr/2017SACLN049

►

Cette thèse vise à contribuer à l'adoption du virtual testing, pratique industrielle encore embryonnaire qui consistera à optimiser et certifier par la simulation numérique le… (more)

▼

Cette thèse vise à contribuer à l'adoption du virtual testing, pratique industrielle encore embryonnaire qui consistera à optimiser et certifier par la simulation numérique le dimensionnement de pièces industrielles critiques. Le virtual testing permettra des économies colossales dans la conception des pièces mécaniques et un plus grand respect de l'environnement grâce à des designs optimisés. Afin d'atteindre un tel objectif, de nouvelles méthodes de calcul doivent être mises en place, plus sûres, plus respectueuses des architectures matérielles, plus rapides, compatibles avec les contraintes temporelles de l'ingénierie. Nous nous intéressons à la résolution parallèle de problèmes non linéaires de grande taille par des méthodes de décomposition de domaine. Notre objectif est d'atteindre une approximation de la solution exacte en minimisant les communications entre les sous-domaines. Pour cela nous souhaitons maximiser les calculs réalisés indépendamment par sous-domaine à l'aide d'approches de relocalisation non linéaire, contrôler les critères de convergence des solveurs imbriqués de manière à éviter la sur-résolution et les divergences, améliorer la construction de conditions d'interface mixtes, et non linéariser l'étape de préconditionnement du solveur. L'objectif à terme étant de traiter des problèmes de complexité industrielle, la robustesse des méthodes sera un souci constant. De manière classique, les problèmes non linéaires sont résolus en construisant une suite de systèmes linéaires qui peuvent être résolus en parallèle à l'aide de méthodes itératives, telles que les solveurs de Krylov. Nous souhaitons remettre en question cette procédure usuelle en essayant de construire une suite de petits systèmes non linéaires indépendants à résoudre en parallèle. Une telle technique implique l'utilisation de solveurs itératifs imbriqués dont les critères de convergence doivent être syntonisés dynamiquement de manière à éviter à la fois la sur-résolution et la perte de convergence. La robustesse de la méthode pourra notamment être assurée par l'emploi de conditions d'interface mixtes bien construites et de préconditionneurs bien choisis.

This thesis is aimed to contribute to the adoption of virtual testing, an industrial practice still embryonic which consists in optimizing and certifying by numerical simulations the dimensioning of critical industrial structures. The virtual testing will allow colossal savings in the design of mechanical parts and a greater respect for the environment, thanks to optimized designs. In order to achieve this goal, new calculation methods must be implemented, satisfying more requirements concerning safety, respect for hardware architectures, fastness, and compatibility with the time constraints of engineering.We are interested in the parallel resolution of large nonlinear problems by domain decomposition methods. Our goal is to approximate the exact solution by minimizing communication between subdomains. In order to do this, we want to maximize the computations performed independently…

Advisors/Committee Members: Rey, Christian (thesis director).

Subjects/Keywords: Mécanique non linéaire; Décomposition de domaine; Conditions d'interface mixtes; Préconditionneur non linéaire; Nonlinear mechanics; Domain decomposition; Mixed interface conditions; Nonlinear preconditioner

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

APA (6^th Edition):

Negrello, C. (2017). Méthodes fortement parallèles pour la simulation numérique en mécanique non linéaire des structures : Highly parallel methods for numerical simulation in nonlinear structural mechanics. (Doctoral Dissertation). Université Paris-Saclay (ComUE). Retrieved from http://www.theses.fr/2017SACLN049

Chicago Manual of Style (16^th Edition):

Negrello, Camille. “Méthodes fortement parallèles pour la simulation numérique en mécanique non linéaire des structures : Highly parallel methods for numerical simulation in nonlinear structural mechanics.” 2017. Doctoral Dissertation, Université Paris-Saclay (ComUE). Accessed April 15, 2021. http://www.theses.fr/2017SACLN049.

MLA Handbook (7^th Edition):

Negrello, Camille. “Méthodes fortement parallèles pour la simulation numérique en mécanique non linéaire des structures : Highly parallel methods for numerical simulation in nonlinear structural mechanics.” 2017. Web. 15 Apr 2021.

Vancouver:

Negrello C. Méthodes fortement parallèles pour la simulation numérique en mécanique non linéaire des structures : Highly parallel methods for numerical simulation in nonlinear structural mechanics. [Internet] [Doctoral dissertation]. Université Paris-Saclay (ComUE); 2017. [cited 2021 Apr 15]. Available from: http://www.theses.fr/2017SACLN049.

Council of Science Editors:

Negrello C. Méthodes fortement parallèles pour la simulation numérique en mécanique non linéaire des structures : Highly parallel methods for numerical simulation in nonlinear structural mechanics. [Doctoral Dissertation]. Université Paris-Saclay (ComUE); 2017. Available from: http://www.theses.fr/2017SACLN049

University of Manchester

24. Rees, Glyn Owen. Efficient ''black-box'' multigrid solvers for convection-dominated problems.

Degree: 2011, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:131408

► The main objective of this project is to develop a ``black-box'' multigrid preconditioner for the iterative solution of finite element discretisations of the convection-diffusion equation… (more)

▼ The main objective of this project is to develop a ``black-box'' multigrid preconditioner for the iterative solution of finite element discretisations of the convection-diffusion equation with dominant convection. This equation can be considered a stand alone scalar problem or as part of a more complex system of partial differential equations, such as the Navier-Stokes equations. The project will focus on the stand alone scalar problem. Multigrid is considered an optimal preconditioner for scalar elliptic problems. This strategy can also be used for convection-diffusion problems, however an appropriate robust smoother needs to be developed to achieve mesh-independent convergence. The focus of the thesis is on the development of such a smoother. In this context a novel smoother is developed referred to as truncated incomplete factorisation (tILU) smoother. In terms of computational complexity and memory requirements, the smoother is considerably less expensive than the standard ILU(0) smoother. At the same time, it exhibits the same robustness as ILU(0) with respect to the problem and discretisation parameters. The new smoother significantly outperforms the standard damped Jacobi smoother and is a competitor to the Gauss-Seidel smoother (and in a number of important cases tILU outperforms the Gauss-Seidel smoother). The new smoother depends on a single parameter (the truncation ratio). The project obtains a default value for this parameter and demonstrated the robust performance of the smoother on a broad range of problems. Therefore, the new smoothing method can be regarded as ``black-box''. Furthermore, the new smoother does not require any particular ordering of the nodes, which is a prerequisite for many robust smoothers developed for convection-dominated convection-diffusion problems. To test the effectiveness of the preconditioning methodology, we consider a number of model problems (in both 2D and 3D) including uniform and complex (recirculating) convection fields discretised by uniform, stretched and adaptively refined grids. The new multigrid preconditioner within block preconditioning of the Navier-Stokes equations was also tested. The numerical results gained during the investigation confirm that tILU is a scalable, robust smoother for both geometric and algebraic multigrid. Also, comprehensive tests show that the tILU smoother is a competitive method. Advisors/Committee Members: Silvester, David, Mihajlovic, Milan.

Subjects/Keywords: Convection-diffusion problem; Multigrid; Preconditioner; Smoother; Incomplete LU factorisation; Finite element method; Black-box; Truncated Incomplete LU factorisation

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

APA (6^th Edition):

Rees, G. O. (2011). Efficient ''black-box'' multigrid solvers for convection-dominated problems. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:131408

Chicago Manual of Style (16^th Edition):

Rees, Glyn Owen. “Efficient ''black-box'' multigrid solvers for convection-dominated problems.” 2011. Doctoral Dissertation, University of Manchester. Accessed April 15, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:131408.

MLA Handbook (7^th Edition):

Rees, Glyn Owen. “Efficient ''black-box'' multigrid solvers for convection-dominated problems.” 2011. Web. 15 Apr 2021.

Vancouver:

Rees GO. Efficient ''black-box'' multigrid solvers for convection-dominated problems. [Internet] [Doctoral dissertation]. University of Manchester; 2011. [cited 2021 Apr 15]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:131408.

Council of Science Editors:

Rees GO. Efficient ''black-box'' multigrid solvers for convection-dominated problems. [Doctoral Dissertation]. University of Manchester; 2011. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:131408

Université de Grenoble

25. Jolivet, Pierre. Méthodes de décomposition de domaine. Application au calcul haute performance : Domain decomposition methods. Application to high-performance computing.

Degree: Docteur es, Mathématiques appliquées, 2014, Université de Grenoble

URL: http://www.theses.fr/2014GRENM040

►

Cette thèse présente une vision unifiée de plusieurs méthodes de décomposition de domaine : celles avec recouvrement, dites de Schwarz, et celles basées sur des… (more)

▼

Cette thèse présente une vision unifiée de plusieurs méthodes de décomposition de domaine : celles avec recouvrement, dites de Schwarz, et celles basées sur des compléments de Schur, dites de sous-structuration. Il est ainsi possible de changer de méthodes de manière abstraite et de construire différents préconditionneurs pour accélérer la résolution de grands systèmes linéaires creux par des méthodes itératives. On rencontre régulièrement ce type de systèmes dans des problèmes industriels ou scientifiques après discrétisation de modèles continus. Bien que de tels préconditionneurs exposent naturellement de bonnes propriétés de parallélisme sur les architectures distribuées, ils peuvent s’avérer être peu performants numériquement pour des décompositions complexes ou des problèmes physiques multi-échelles. On peut pallier ces défauts de robustesse en calculant de façon concurrente des problèmes locaux creux ou denses aux valeurs propres généralisées. D’aucuns peuvent alors identifier des modes qui perturbent la convergence des méthodes itératives sous-jacentes a priori. En utilisant ces modes, il est alors possible de définir des opérateurs de projection qui utilisent un problème dit grossier. L’utilisation de ces outils auxiliaires règle généralement les problèmes sus-cités, mais tend à diminuer les performances algorithmiques des préconditionneurs. Dans ce manuscrit, on montre en trois points quela nouvelle construction développée est performante : 1) grâce à des essais numériques à très grande échelle sur Curie—un supercalculateur européen, puis en le comparant à des solveurs de pointe 2) multi-grilles et 3) directs.

This thesis introduces a unified framework for various domain decomposition methods:those with overlap, so-called Schwarz methods, and those based on Schur complements,so-called substructuring methods. It is then possible to switch with a high-level of abstractionbetween methods and to build different preconditioners to accelerate the iterativesolution of large sparse linear systems. Such systems are frequently encountered in industrialor scientific problems after discretization of continuous models. Even though thesepreconditioners naturally exhibit good parallelism properties on distributed architectures,they can prove inadequate numerical performance for complex decompositions or multiscalephysics. This lack of robustness may be alleviated by concurrently solving sparse ordense local generalized eigenvalue problems, thus identifying modes that hinder the convergenceof the underlying iterative methods a priori. Using these modes, it is then possibleto define projection operators based on what is usually referred to as a coarse solver. Theseauxiliary tools tend to solve the aforementioned issues, but typically decrease the parallelefficiency of the preconditioners. In this dissertation, it is shown in three points thatthe newly developed construction is efficient: 1) by performing large-scale numerical experimentson Curie—a European supercomputer, and by comparing it with state of the art2)…

Advisors/Committee Members: Prud'homme, Christophe (thesis director), Nataf, Frédéric (thesis director).

Subjects/Keywords: Algèbre linéaire; Préconditionneur; Calcul haute performance; Décomposition de domaine; Linear algebra; Preconditioner; High-performance computing; Domain decomposition; 510

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

APA (6^th Edition):

Jolivet, P. (2014). Méthodes de décomposition de domaine. Application au calcul haute performance : Domain decomposition methods. Application to high-performance computing. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2014GRENM040

Chicago Manual of Style (16^th Edition):

Jolivet, Pierre. “Méthodes de décomposition de domaine. Application au calcul haute performance : Domain decomposition methods. Application to high-performance computing.” 2014. Doctoral Dissertation, Université de Grenoble. Accessed April 15, 2021. http://www.theses.fr/2014GRENM040.

MLA Handbook (7^th Edition):

Jolivet, Pierre. “Méthodes de décomposition de domaine. Application au calcul haute performance : Domain decomposition methods. Application to high-performance computing.” 2014. Web. 15 Apr 2021.

Vancouver:

Jolivet P. Méthodes de décomposition de domaine. Application au calcul haute performance : Domain decomposition methods. Application to high-performance computing. [Internet] [Doctoral dissertation]. Université de Grenoble; 2014. [cited 2021 Apr 15]. Available from: http://www.theses.fr/2014GRENM040.

Council of Science Editors:

Jolivet P. Méthodes de décomposition de domaine. Application au calcul haute performance : Domain decomposition methods. Application to high-performance computing. [Doctoral Dissertation]. Université de Grenoble; 2014. Available from: http://www.theses.fr/2014GRENM040

Univerzitet u Beogradu

26. Mirkov, Nikola S. 1982-. Нумеричка симулација турбулентних струјања над реалним комплексним теренима.

Degree: Mašinski fakultet, 2016, Univerzitet u Beogradu

URL: https://fedorabg.bg.ac.rs/fedora/get/o:11633/bdef:Content/get

►

Техничке науке - Машинство / Technical sciences - Mechanical Engineering

У дисертацији је представљена нова и унапређена прорачунска проце- дура базирана на методи коначних запремина,… (more)

▼

Техничке науке - Машинство / Technical sciences - Mechanical Engineering

У дисертацији је представљена нова и унапређена прорачунска проце- дура базирана на методи коначних запремина, која је развијена за потребе симулације турбулентних ваздушних струјања над реалним комплексним теренима. У дисертацији су разматране ефикасна апроксимација ковекције, дифузних чланова, реконструкција ћелијски-центрираних градијената, спре- зање поља притиска и брзине преко SIMPLE алгоритма са вишеструком ре- шавањем једначине за корекцију притиска у секвенци корака неортогонал- них корекција. Од постојећих компонетни алгоритма биране су оне које су показале способност за унапређени третман неортогоналности на ћелијском нивоу, унутар прорачунске мреже, а на местима на којима је сматрано по- требно уведене су оригиналне формулације како би се тачност прорачуна и нумеричка ефикасност унапредиле за дати тип струјања и представљају оригинални научни допринос ове дисертације. Посебно су обрађене сле- деће теме: i) процедура реконструкције ћелијски ценрираних градијената, укључујући и третман градијената притиска, ii) нови генерализивани при- ступ апроксимацији дифузионог члана, примењивог у присуству израже- них деформација прорачунске мреже. Више нумеричких експеримената је приказано да би се демонстрирала прорачунска прецизност и ефикасност предложене методе. Верификација нумеричког алгоритма је извршена на примерима различитог нивоа ком- плексности и намене. Почиње се реконструкцијом једноставних синтетич- ких функција, осмишљених да истакну одређене недостатке постојећих ал- горитама за струјања у изразито неортогоналним геометријама. Тестови су такође извршени на аналитичким решењима Навије-Стоксових једначина, затим су приказани резултати поређења са другим нумеричким симулаци- јама, изведених са сличним алгоритмима, вршена су поређења са резулта- тима испитивања у аеротунелима, и напокон вршена су поређења симула- ција са мерењима над реалним комплексним брдовитим теренима у реал- ном, атмосферском окружењу. Нумерички експерименти показују да су постигнута значајна унапре- ђења са предложеном нумеричком процедуром, у односу на конвенционалне нумеричке процедуре. Тестови апроксимације ћелијски центрираних гра- дијената користећи синтетичка решења су показали да је предложени при- ступ способан да оствари поклапање на нивоу рачунарске прецизности, чак и на изузетно деформисаним мрежама. У тестовима који укључују стру- јања са аналитичким решењима, метод је показао очекивани други ред тач- ности на униформним праволинијским мрежама. На деформисаним мре- жама, нове шеме за дискретизацију дифузије су показале значајно побољ- шање како у прецизности прорачуна, тако и у брзини конвергенције, у по- ређењу са другим приступима који су такође укључивали корекције неор- тогоналности. Резултати су показали да није довољно узети у обзир само искошеност прорачунских ћелија унутар мреже, већ да је потребно узети у обзир појам отклона тачке пресека, који је дефинисан у овој дисертацији, уколико постоји потреба за већом прецизношћу прорачуна. Једно…

Advisors/Committee Members: Rašuo, Boško, 1949-.

Subjects/Keywords: finite volume method; unsteady incompressible flow; cell-centered approach; pressurecorrection; preconditioner; non-orthogonal grids; complex terrain

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❌

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

APA (6^th Edition):

Mirkov, N. S. 1. (2016). Нумеричка симулација турбулентних струјања над реалним комплексним теренима. (Thesis). Univerzitet u Beogradu. Retrieved from https://fedorabg.bg.ac.rs/fedora/get/o:11633/bdef:Content/get

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):

Mirkov, Nikola S 1982-. “Нумеричка симулација турбулентних струјања над реалним комплексним теренима.” 2016. Thesis, Univerzitet u Beogradu. Accessed April 15, 2021. https://fedorabg.bg.ac.rs/fedora/get/o:11633/bdef:Content/get.

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

MLA Handbook (7^th Edition):

Mirkov, Nikola S 1982-. “Нумеричка симулација турбулентних струјања над реалним комплексним теренима.” 2016. Web. 15 Apr 2021.

Vancouver:

Mirkov NS1. Нумеричка симулација турбулентних струјања над реалним комплексним теренима. [Internet] [Thesis]. Univerzitet u Beogradu; 2016. [cited 2021 Apr 15]. Available from: https://fedorabg.bg.ac.rs/fedora/get/o:11633/bdef:Content/get.

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

Council of Science Editors:

Mirkov NS1. Нумеричка симулација турбулентних струјања над реалним комплексним теренима. [Thesis]. Univerzitet u Beogradu; 2016. Available from: https://fedorabg.bg.ac.rs/fedora/get/o:11633/bdef:Content/get

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

University of Manchester

27. Rees, Glyn Owen. Efficient "black-box" multigrid solvers for convection-dominated problems.

Degree: PhD, 2011, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/efficient-blackbox-multigrid-solvers-for-convectiondominated-problems(d49ec3ea-1dc2-4238-b0c1-0688e5944ddd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542777

► The main objective of this project is to develop a "black-box" multigrid preconditioner for the iterative solution of finite element discretisations of the convection-diffusion equation… (more)

▼ The main objective of this project is to develop a "black-box" multigrid preconditioner for the iterative solution of finite element discretisations of the convection-diffusion equation with dominant convection. This equation can be considered a stand alone scalar problem or as part of a more complex system of partial differential equations, such as the Navier-Stokes equations. The project will focus on the stand alone scalar problem. Multigrid is considered an optimal preconditioner for scalar elliptic problems. This strategy can also be used for convection-diffusion problems, however an appropriate robust smoother needs to be developed to achieve mesh-independent convergence. The focus of the thesis is on the development of such a smoother. In this context a novel smoother is developed referred to as truncated incomplete factorisation (tILU) smoother. In terms of computational complexity and memory requirements, the smoother is considerably less expensive than the standard ILU(0) smoother. At the same time, it exhibits the same robustness as ILU(0) with respect to the problem and discretisation parameters. The new smoother significantly outperforms the standard damped Jacobi smoother and is a competitor to the Gauss-Seidel smoother (and in a number of important cases tILU outperforms the Gauss-Seidel smoother). The new smoother depends on a single parameter (the truncation ratio). The project obtains a default value for this parameter and demonstrated the robust performance of the smoother on a broad range of problems. Therefore, the new smoothing method can be regarded as "black-box". Furthermore, the new smoother does not require any particular ordering of the nodes, which is a prerequisite for many robust smoothers developed for convection-dominated convection-diffusion problems. To test the effectiveness of the preconditioning methodology, we consider a number of model problems (in both 2D and 3D) including uniform and complex (recirculating) convection fields discretised by uniform, stretched and adaptively refined grids. The new multigrid preconditioner within block preconditioning of the Navier-Stokes equations was also tested. The numerical results gained during the investigation confirm that tILU is a scalable, robust smoother for both geometric and algebraic multigrid. Also, comprehensive tests show that the tILU smoother is a competitive method.

Subjects/Keywords: 519; Convection-diffusion problem; Multigrid; Preconditioner; Smoother; Incomplete LU factorisation; Finite element method; Black-box; Truncated Incomplete LU factorisation

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

APA (6^th Edition):

Rees, G. O. (2011). Efficient "black-box" multigrid solvers for convection-dominated problems. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/efficient-blackbox-multigrid-solvers-for-convectiondominated-problems(d49ec3ea-1dc2-4238-b0c1-0688e5944ddd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542777

Chicago Manual of Style (16^th Edition):

Rees, Glyn Owen. “Efficient "black-box" multigrid solvers for convection-dominated problems.” 2011. Doctoral Dissertation, University of Manchester. Accessed April 15, 2021. https://www.research.manchester.ac.uk/portal/en/theses/efficient-blackbox-multigrid-solvers-for-convectiondominated-problems(d49ec3ea-1dc2-4238-b0c1-0688e5944ddd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542777.

MLA Handbook (7^th Edition):

Rees, Glyn Owen. “Efficient "black-box" multigrid solvers for convection-dominated problems.” 2011. Web. 15 Apr 2021.

Vancouver:

Rees GO. Efficient "black-box" multigrid solvers for convection-dominated problems. [Internet] [Doctoral dissertation]. University of Manchester; 2011. [cited 2021 Apr 15]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/efficient-blackbox-multigrid-solvers-for-convectiondominated-problems(d49ec3ea-1dc2-4238-b0c1-0688e5944ddd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542777.

Council of Science Editors:

Rees GO. Efficient "black-box" multigrid solvers for convection-dominated problems. [Doctoral Dissertation]. University of Manchester; 2011. Available from: https://www.research.manchester.ac.uk/portal/en/theses/efficient-blackbox-multigrid-solvers-for-convectiondominated-problems(d49ec3ea-1dc2-4238-b0c1-0688e5944ddd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542777

New Jersey Institute of Technology

28. Bandegi, Mahdi. Convex relaxations of a continuum aggregation model, and their efficient numerical solution.

Degree: PhD, Mathematical Sciences, 2019, New Jersey Institute of Technology

URL: https://digitalcommons.njit.edu/dissertations/1430

► In this dissertation, the global minimization of a large deviations rate function (the Helmholtz free energy functional) for the Boltzmann distribution is discussed. The… (more)

Subjects/Keywords: Continuum aggregation model; Convex relaxations; Global minimization; Helmholtz free energy functional; Matrix-free interior-point method; Preconditioner; Mathematics

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

APA (6^th Edition):

Bandegi, M. (2019). Convex relaxations of a continuum aggregation model, and their efficient numerical solution. (Doctoral Dissertation). New Jersey Institute of Technology. Retrieved from https://digitalcommons.njit.edu/dissertations/1430

Chicago Manual of Style (16^th Edition):

Bandegi, Mahdi. “Convex relaxations of a continuum aggregation model, and their efficient numerical solution.” 2019. Doctoral Dissertation, New Jersey Institute of Technology. Accessed April 15, 2021. https://digitalcommons.njit.edu/dissertations/1430.

MLA Handbook (7^th Edition):

Bandegi, Mahdi. “Convex relaxations of a continuum aggregation model, and their efficient numerical solution.” 2019. Web. 15 Apr 2021.

Vancouver:

Bandegi M. Convex relaxations of a continuum aggregation model, and their efficient numerical solution. [Internet] [Doctoral dissertation]. New Jersey Institute of Technology; 2019. [cited 2021 Apr 15]. Available from: https://digitalcommons.njit.edu/dissertations/1430.

Council of Science Editors:

Bandegi M. Convex relaxations of a continuum aggregation model, and their efficient numerical solution. [Doctoral Dissertation]. New Jersey Institute of Technology; 2019. Available from: https://digitalcommons.njit.edu/dissertations/1430

Delft University of Technology

29. Diao, H. (author). Fourier Analysis of Iterative Methods for the Helmholtz Problem.

Degree: 2012, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

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This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues… (more)

Subjects/Keywords: Helmholtz problem; Krylov subspace methods; multigrid method; multilevel Krylov multigrid method; shifted Laplacian preconditioner; deflation operator; Fourier analysis

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

APA (6^th Edition):

Diao, H. (. (2012). Fourier Analysis of Iterative Methods for the Helmholtz Problem. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

Chicago Manual of Style (16^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Masters Thesis, Delft University of Technology. Accessed April 15, 2021. http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

MLA Handbook (7^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Web. 15 Apr 2021.

Vancouver:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Internet] [Masters thesis]. Delft University of Technology; 2012. [cited 2021 Apr 15]. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

Council of Science Editors:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Masters Thesis]. Delft University of Technology; 2012. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

Michigan Technological University

30. Azzam, Joy. Sub-Sampled Matrix Approximations.

Degree: PhD, Department of Mathematical Sciences, 2020, Michigan Technological University

URL: https://digitalcommons.mtu.edu/etdr/1002

► Matrix approximations are widely used to accelerate many numerical algorithms. Current methods sample row (or column) spaces to reduce their computational footprint and approximate… (more)

Subjects/Keywords: Matrix Approximation; Inverse Matrix Approximation; Low Rank Approximation; Quasi-Newton; Randomized Numerical Linear Algebra; Preconditioner; Sub-Sampled; Other Applied Mathematics

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

APA (6^th Edition):

Azzam, J. (2020). Sub-Sampled Matrix Approximations. (Doctoral Dissertation). Michigan Technological University. Retrieved from https://digitalcommons.mtu.edu/etdr/1002

Chicago Manual of Style (16^th Edition):

Azzam, Joy. “Sub-Sampled Matrix Approximations.” 2020. Doctoral Dissertation, Michigan Technological University. Accessed April 15, 2021. https://digitalcommons.mtu.edu/etdr/1002.

MLA Handbook (7^th Edition):

Azzam, Joy. “Sub-Sampled Matrix Approximations.” 2020. Web. 15 Apr 2021.

Vancouver:

Azzam J. Sub-Sampled Matrix Approximations. [Internet] [Doctoral dissertation]. Michigan Technological University; 2020. [cited 2021 Apr 15]. Available from: https://digitalcommons.mtu.edu/etdr/1002.

Council of Science Editors:

Azzam J. Sub-Sampled Matrix Approximations. [Doctoral Dissertation]. Michigan Technological University; 2020. Available from: https://digitalcommons.mtu.edu/etdr/1002

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Open Access Theses and Dissertations