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340 results on '"Rheinbach, Oliver"'

1. A Comparison Of Direct Solvers In FROSch Applied To Chemo-Mechanics

Author

Heinlein, Alexander, Kiefer, Bjoern, Prüger, Stefan, Rheinbach, Oliver, and Röver, Friederike

Subjects
Mathematics - Numerical Analysis, Computer Science - Distributed, Parallel, and Cluster Computing
Abstract

Sparse direct linear solvers are at the computational core of domain decomposition preconditioners and therefore have a strong impact on their performance. In this paper, we consider the Fast and Robust Overlapping Schwarz (FROSch) solver framework of the Trilinos software library, which contains a parallel implementations of the GDSW domain decomposition preconditioner. We compare three different sparse direct solvers used to solve the subdomain problems in FROSch. The preconditioner is applied to different model problems; linear elasticity and more complex fully-coupled deformation diffusion-boundary value problems from chemo-mechanics. We employ FROSch in fully algebraic mode, and therefore, we do not expect numerical scalability. Strong scalability is studied from 64 to 4096 cores, where good scaling results are obtained up to 1728 cores. The increasing size of the coarse problem increases the solution time for all sparse direct solvers.

Published
2023

2. A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods

Author

Balzani, Daniel, Heinlein, Alexander, Klawonn, Axel, Knepper, Jascha, Ramesh, Sharan Nurani, Rheinbach, Oliver, Sassmannshausen, Lea, and Uhlmann, Klemens

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, Computer Science - Distributed, Parallel, and Cluster Computing, 65N55, 6504, 65F08, 7404, 7410, 74F25
Abstract

A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja-Smith-Widlund) and RDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed.

Published
2023

3. Monolithic parallel overlapping Schwarz methods in fully-coupled nonlinear chemo-mechanics problems

Author

Kiefer, Bjoern, Prüger, Stefan, Rheinbach, Oliver, and Röver, Friederike

Subjects
Mathematics - Numerical Analysis, 65M55, 74F25
Abstract

We consider the swelling of hydrogels as an example of a chemo-mechanical problem with strong coupling between the mechanical balance relations and the mass diffusion. The problem is cast into a minimization formulation using a time-explicit approach for the dependency of the dissipation potential on the deformation and the swelling volume fraction to obtain symmetric matrices, which are typically better suited for iterative solvers. The MPI-parallel implementation uses the software libraries deal.II, p4est and FROSch (Fast of Robust Overlapping Schwarz). FROSch is part of the Trilinos library and is used in fully algebraic mode, i.e., the preconditioner is constructed from the monolithic system matrix without making explicit use of the problem structure. Strong and weak parallel scalability is studied using up to 512 cores, considering the standard GDSW (Generalized Dryja-Smith-Widlund) coarse space and the newer coarse space with reduced dimension. The FROSch solver is applicable to the coupled problems within in the range of processor cores considered here, although numerical scalablity cannot be expected (and is not observed) for the fully algebraic mode. In our strong scalability study, the average number of Krylov iterations per Newton iteration is higher by a factor of up to six compared to a linear elasticity problem. However, making mild use of the problem structure in the preconditioner, this number can be reduced to a factor of two and, importantly, also numerical scalability can then be achieved experimentally. Nevertheless, the fully algebraic mode is still preferable since a faster time to solution is achieved.

Published
2022

4. Composing Two Different Nonlinear FETI–DP Methods

Author

Kohler, Stephan, Rheinbach, Oliver, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Dostál, Zdeněk, editor, Kozubek, Tomáš, editor, Klawonn, Axel, editor, Langer, Ulrich, editor, Pavarino, Luca F., editor, Šístek, Jakub, editor, and Widlund, Olof B., editor

Published
2024
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6. A Three-Level Extension for Fast and Robust Overlapping Schwarz (FROSch) Preconditioners with Reduced Dimensional Coarse Space

Author

Heinlein, Alexander, Klawonn, Axel, Rheinbach, Oliver, Röver, Friederike, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Brenner, Susanne C., editor, Chung, Eric, editor, Klawonn, Axel, editor, Kwok, Felix, editor, Xu, Jinchao, editor, and Zou, Jun, editor

Published
2022
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9. Logistic Regression for Prospectivity Modeling

Author

Kost, Samuel, Rheinbach, Oliver, Schaeben, Helmut, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Vermolen, Fred J., editor, and Vuik, Cornelis, editor

Published
2021
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13. A Closer Look at Local Eigenvalue Solvers for Adaptive FETI-DP and BDDC

Author

Klawonn, Axel, Kühn, Martin J., Rheinbach, Oliver, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Haynes, Ronald, editor, MacLachlan, Scott, editor, Cai, Xiao-Chuan, editor, Halpern, Laurence, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, and Widlund, Olof, editor

Published
2020
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14. FROSch: A Fast And Robust Overlapping Schwarz Domain Decomposition Preconditioner Based on Xpetra in Trilinos

Author

Heinlein, Alexander, Klawonn, Axel, Rajamanickam, Sivasankaran, Rheinbach, Oliver, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Haynes, Ronald, editor, MacLachlan, Scott, editor, Cai, Xiao-Chuan, editor, Halpern, Laurence, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, and Widlund, Olof, editor

Published
2020
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15. A Three-level Extension of the GDSW Overlapping Schwarz Preconditioner in Three Dimensions

Author

Heinlein, Alexander, Klawonn, Axel, Rheinbach, Oliver, Röver, Friederike, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Haynes, Ronald, editor, MacLachlan, Scott, editor, Cai, Xiao-Chuan, editor, Halpern, Laurence, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, and Widlund, Olof, editor

Published
2020
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16. EXASTEEL: Towards a Virtual Laboratory for the Multiscale Simulation of Dual-Phase Steel Using High-Performance Computing

Author

Klawonn, Axel, Lanser, Martin, Uran, Matthias, Rheinbach, Oliver, Köhler, Stephan, Schröder, Jörg, Scheunemann, Lisa, Brands, Dominik, Balzani, Daniel, Gandhi, Ashutosh, Wellein, Gerhard, Wittmann, Markus, Schenk, Olaf, Janalík, Radim, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bungartz, Hans-Joachim, editor, Reiz, Severin, editor, Uekermann, Benjamin, editor, Neumann, Philipp, editor, and Nagel, Wolfgang E., editor

Published
2020
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17. A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods

Author

Balzani, Daniel (author), Heinlein, A. (author), Klawonn, Axel (author), Knepper, Jascha (author), Nurani Ramesh, Sharan (author), Rheinbach, Oliver (author), Saßmannshausen, Lea (author), Uhlmann, Klemens (author), Balzani, Daniel (author), Heinlein, A. (author), Klawonn, Axel (author), Knepper, Jascha (author), Nurani Ramesh, Sharan (author), Rheinbach, Oliver (author), Saßmannshausen, Lea (author), and Uhlmann, Klemens (author)

Abstract

A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed., Numerical Analysis

Published
2024
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18. A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions

Author

Heinlein, Alexander, Klawonn, Axel, Rheinbach, Oliver, Röver, Friederike, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Apel, Thomas, editor, Langer, Ulrich, editor, Meyer, Arnd, editor, and Steinbach, Olaf, editor

Published
2019
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21. Using Algebraic Multigrid in Inexact BDDC Domain Decomposition Methods

Author

Klawonn, Axel, Lanser, Martin, Rheinbach, Oliver, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bjørstad, Petter E., editor, Brenner, Susanne C., editor, Halpern, Lawrence, editor, Kim, Hyea Hyun, editor, Kornhuber, Ralf, editor, Rahman, Talal, editor, and Widlund, Olof B., editor

Published
2018
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22. On the Accuracy of the Inner Newton Iteration in Nonlinear Domain Decomposition

Author

Klawonn, Axel, Lanser, Martin, Rheinbach, Oliver, Uran, Matthias, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bjørstad, Petter E., editor, Brenner, Susanne C., editor, Halpern, Lawrence, editor, Kim, Hyea Hyun, editor, Kornhuber, Ralf, editor, Rahman, Talal, editor, and Widlund, Olof B., editor

Published
2018
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23. Preconditioning of Iterative Eigenvalue Problem Solvers in Adaptive FETI-DP

Author

Klawonn, Axel, Kühn, Martin, Rheinbach, Oliver, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bjørstad, Petter E., editor, Brenner, Susanne C., editor, Halpern, Lawrence, editor, Kim, Hyea Hyun, editor, Kornhuber, Ralf, editor, Rahman, Talal, editor, and Widlund, Olof B., editor

Published
2018
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24. Improving the Parallel Performance of Overlapping Schwarz Methods by Using a Smaller Energy Minimizing Coarse Space

Author

Heinlein, Alexander, Klawonn, Axel, Rheinbach, Oliver, Widlund, Olof B., Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bjørstad, Petter E., editor, Brenner, Susanne C., editor, Halpern, Lawrence, editor, Kim, Hyea Hyun, editor, Kornhuber, Ralf, editor, Rahman, Talal, editor, and Widlund, Olof B., editor

Published
2018
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25. An Adaptive GDSW Coarse Space for Two-Level Overlapping Schwarz Methods in Two Dimensions

Author

Heinlein, Alexander, Klawonn, Axel, Knepper, Jascha, Rheinbach, Oliver, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bjørstad, Petter E., editor, Brenner, Susanne C., editor, Halpern, Lawrence, editor, Kim, Hyea Hyun, editor, Kornhuber, Ralf, editor, Rahman, Talal, editor, and Widlund, Olof B., editor

Published
2018
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27. Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space

Author

Heinlein, Alexander, Klawonn, Axel, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Lee, Chang-Ock, editor, Cai, Xiao-Chuan, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, Park, Eun-Jae, editor, and Widlund, Olof B., editor

Published
2017
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28. Newton-Krylov-FETI-DP with Adaptive Coarse Spaces

Author

Klawonn, Axel, Lanser, Martin, Niehoff, Balthasar, Radtke, Patrick, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Lee, Chang-Ock, editor, Cai, Xiao-Chuan, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, Park, Eun-Jae, editor, and Widlund, Olof B., editor

Published
2017
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29. New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables

Author

Klawonn, Axel, Lanser, Martin, Rheinbach, Oliver, Uran, Matthias, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Lee, Chang-Ock, editor, Cai, Xiao-Chuan, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, Park, Eun-Jae, editor, and Widlund, Olof B., editor

Published
2017
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30. Adaptive Coarse Spaces for FETI-DP in Three Dimensions with Applications to Heterogeneous Diffusion Problems

Author

Klawonn, Axel, Kühn, Martin, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Lee, Chang-Ock, editor, Cai, Xiao-Chuan, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, Park, Eun-Jae, editor, and Widlund, Olof B., editor

Published
2017
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31. EXASTEEL: Towards a Virtual Laboratory for the Multiscale Simulation of Dual-Phase Steel Using High-Performance Computing

Author

Klawonn, Axel, primary, Lanser, Martin, additional, Uran, Matthias, additional, Rheinbach, Oliver, additional, Köhler, Stephan, additional, Schröder, Jörg, additional, Scheunemann, Lisa, additional, Brands, Dominik, additional, Balzani, Daniel, additional, Gandhi, Ashutosh, additional, Wellein, Gerhard, additional, Wittmann, Markus, additional, Schenk, Olaf, additional, and Janalík, Radim, additional

Published
2020
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32. Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks

Author

Baker, Allison H., Klawonn, Axel, Kolev, Tzanio, Lanser, Martin, Rheinbach, Oliver, Yang, Ulrike Meier, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Bungartz, Hans-Joachim, editor, Neumann, Philipp, editor, and Nagel, Wolfgang E., editor

Published
2016
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33. One-Way and Fully-Coupled FE2 Methods for Heterogeneous Elasticity and Plasticity Problems: Parallel Scalability and an Application to Thermo-Elastoplasticity of Dual-Phase Steels

Author

Balzani, Daniel, Gandhi, Ashutosh, Klawonn, Axel, Lanser, Martin, Rheinbach, Oliver, Schröder, Jörg, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Bungartz, Hans-Joachim, editor, Neumann, Philipp, editor, and Nagel, Wolfgang E., editor

Published
2016
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34. Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction

Author

Heinlein, Alexander, Klawonn, Axel, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Karasözen, Bülent, editor, Manguoğlu, Murat, editor, Tezer-Sezgin, Münevver, editor, Göktepe, Serdar, editor, and Uğur, Ömür, editor

Published
2016
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35. A Highly Scalable Implementation of Inexact Nonlinear FETI-DP Without Sparse Direct Solvers

Author

Klawonn, Axel, Lanser, Martin, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Karasözen, Bülent, editor, Manguoğlu, Murat, editor, Tezer-Sezgin, Münevver, editor, Göktepe, Serdar, editor, and Uğur, Ömür, editor

Published
2016
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36. A Newton-Krylov-FETI-DP Method with an Adaptive Coarse Space Applied to Elastoplasticity

Author

Klawonn, Axel, Radtke, Patrick, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
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37. Adaptive Coarse Spaces for BDDC with a Transformation of Basis

Author

Klawonn, Axel, Radtke, Patrick, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
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38. A Nonlinear FETI-DP Method with an Inexact Coarse Problem

Author

Klawonn, Axel, Lanser, Martin, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
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39. Hybrid MPI/OpenMP Parallelization in FETI-DP Methods

Author

Klawonn, Axel, Lanser, Martin, Rheinbach, Oliver, Stengel, Holger, Wellein, Gerhard, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Mehl, Miriam, editor, Bischoff, Manfred, editor, and Schäfer, Michael, editor

Published
2015
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40. A Deflation Based Coarse Space in Dual-Primal FETI Methods for Almost Incompressible Elasticity

Author

Gippert, Sabrina, Klawonn, Axel, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Abdulle, Assyr, editor, Deparis, Simone, editor, Kressner, Daniel, editor, Nobile, Fabio, editor, and Picasso, Marco, editor

Published
2015
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41. A Multilevel Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions

Author

Heinlein, A. (author), Rheinbach, Oliver (author), Röver, Friederike (author), Heinlein, A. (author), Rheinbach, Oliver (author), and Röver, Friederike (author)

Abstract

Multilevel extensions of overlapping Schwarz domain decomposition preconditioners of Generalized Dryja-Smith-Widlund (GDSW) type are considered in this paper. The original GDSW preconditioner is a two-level overlapping Schwarz domain decomposition preconditioner, which can be constructed algebraically from the fully assembled stiffness matrix. The FROSch software, which belongs to the ShyLU package of the Trilinos software library, provides parallel implementations of different variants of GDSW preconditioners. The coarse problem can limit the parallel scalability of two-level GDSW preconditioners. As a remedy, in the past, three-level GDSW approaches have been proposed, which can significantly extend the range of scalability. Here, a multilevel extension of the GDSW preconditioner is introduced and analyzed. Finally, parallel results for the implementation in FROSch for up to 40 000 cores of the SuperMUC-NG supercomputer at Leibniz Supercomputing Centre (LRZ) and to 48 000 cores of the JUWELS supercomputer at Jülich Supercomputing Centre (JSC) are presented., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Numerical Analysis

Published
2023
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42. FETI-DP Methods for Optimal Control Problems

Author

Herzog, Roland, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
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43. On an Adaptive Coarse Space and on Nonlinear Domain Decomposition

Author

Klawonn, Axel, Lanser, Martin, Radtke, Patrick, Rheinbach, Oliver, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
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49. A Multilevel Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions.

Author

Heinlein, Alexander, Rheinbach, Oliver, and Röver, Friederike

Subjects
SCALABILITY, INTEGRATED software
Abstract

Multilevel extensions of overlapping Schwarz domain decomposition preconditioners of Generalized Dryja–Smith–Widlund (GDSW) type are considered in this paper. The original GDSW preconditioner is a two-level overlapping Schwarz domain decomposition preconditioner, which can be constructed algebraically from the fully assembled stiffness matrix. The FROSch software, which belongs to the ShyLU package of the Trilinos software library, provides parallel implementations of different variants of GDSW preconditioners. The coarse problem can limit the parallel scalability of two-level GDSW preconditioners. As a remedy, in the past, three-level GDSW approaches have been proposed, which can significantly extend the range of scalability. Here, a multilevel extension of the GDSW preconditioner is introduced and analyzed. Finally, parallel results for the implementation in FROSch for up to 40 000 cores of the SuperMUC-NG supercomputer at Leibniz Supercomputing Centre (LRZ) and to 48 000 cores of the JUWELS supercomputer at Jülich Supercomputing Centre (JSC) are presented. [ABSTRACT FROM AUTHOR]

Published
2023
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