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Journal Article
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Wasiak, Adam
ORCID: 0000-0002-5705-9754
(2023).
Adaptive and Frugal FETI-DP for Virtual Elements.
Vietnam J. Math., 51 (1).
S. 89 - 112.
SINGAPORE:
SPRINGER SINGAPORE PTE LTD.
ISSN 2305-2228
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Knepper, Jascha
ORCID: 0000-0002-8769-2235, Rheinbach, Oliver
ORCID: 0000-0002-9310-8533 and Widlund, Olof B.
(2022).
ADAPTIVE GDSW COARSE SPACES OF REDUCED DIMENSION FOR OVERLAPPING SCHWARZ METHODS.
SIAM J. Sci. Comput., 44 (3).
S. A1176 - 29.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Grimm, Viktor ORCID: 0000-0001-5300-3705, Heinlein, Alexander
ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
ORCID: 0000-0002-6692-2230
(2022).
ESTIMATING THE TIME-DEPENDENT CONTACT RATE OF SIR AND SEIR MODELS IN MATHEMATICAL EPIDEMIOLOGY USING PHYSICS-INFORMED NEURAL NETWORKS.
Electron. Trans. Numer. Anal., 56.
S. 1 - 28.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2021).
COMBINING MACHINE LEARNING AND ADAPTIVE COARSE SPACES---A HYBRID APPROACH FOR ROBUST FETI-DP METHODS IN THREE DIMENSIONS.
SIAM J. Sci. Comput., 43 (5).
S. S816 - 23.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver
ORCID: 0000-0002-9310-8533 and Uran, Matthias
(2021).
Fully-coupled micro-macro finite element simulations of the Nakajima test using parallel computational homogenization.
Comput. Mech., 68 (5).
S. 1153 - 1179.
NEW YORK:
SPRINGER.
ISSN 1432-0924
Klawonn, Axel ORCID: 0000-0003-4765-7387, Koehler, Stephan, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2020).
Computational homogenization with million-way parallelism using domain decomposition methods.
Comput. Mech., 65 (1).
S. 1 - 23.
NEW YORK:
SPRINGER.
ISSN 1432-0924
Klawonn, Axel ORCID: 0000-0003-4765-7387, Kuhn, Martin J.
ORCID: 0000-0002-0906-6984 and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2020).
Parallel adaptive FETI-DP using lightweight asynchronous dynamic load balancing.
Int. J. Numer. Methods Eng., 121 (4).
S. 621 - 644.
HOBOKEN:
WILEY.
ISSN 1097-0207
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2020).
Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems.
Int. J. Numer. Methods Eng., 121 (6).
S. 1101 - 1120.
HOBOKEN:
WILEY.
ISSN 1097-0207
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Knepper, Jascha and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2019).
ADAPTIVE GDSW COARSE SPACES FOR OVERLAPPING SCHWARZ METHODS IN THREE DIMENSIONS.
SIAM J. Sci. Comput., 41 (5).
S. A3045 - 28.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2019).
MACHINE LEARNING IN ADAPTIVE DOMAIN DECOMPOSITION METHODS-PREDICTING THE GEOMETRIC LOCATION OF CONSTRAINTS.
SIAM J. Sci. Comput., 41 (6).
S. A3887 - 26.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2019).
MONOLITHIC OVERLAPPING SCHWARZ DOMAIN DECOMPOSITION METHODS WITH GDSW COARSE SPACES FOR INCOMPRESSIBLE FLUID FLOW PROBLEMS.
SIAM J. Sci. Comput., 41 (4).
S. C291 - 26.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver and Weber, Janine
(2019).
PRECONDITIONING THE COARSE PROBLEM OF BDDC METHODS-THREE-LEVEL, ALGEBRAIC MULTIGRID, AND VERTEX-BASED PRECONDITIONERS.
Electron. Trans. Numer. Anal., 51.
S. 432 - 451.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Klawonn, Axel ORCID: 0000-0003-4765-7387, Kuehn, Martin and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2018).
ADAPTIVE FETI-DP AND BDDC METHODS WITH A GENERALIZED TRANSFORMATION OF BASIS FOR HETEROGENEOUS PROBLEMS.
Electron. Trans. Numer. Anal., 49.
S. 1 - 28.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Brenner, Susanne, Cai, Xiao-Chuan, Gander, Martin J., Klawonn, Axel ORCID: 0000-0003-4765-7387, Sarkis, Marcus and Szyld, Daniel B.
(2018).
Dedicated to Olof B. Widlund on the occasion of his 80th birthday.
Electron. Trans. Numer. Anal., 49.
S. VII - 2.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Knepper, Jascha and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2018).
MULTISCALE COARSE SPACES FOR OVERLAPPING SCHWARZ METHODS BASED ON THE ACMS SPACE IN 2D.
Electron. Trans. Numer. Anal., 48.
S. 156 - 183.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2018).
NONLINEAR BDDC METHODS WITH APPROXIMATE SOLVERS.
Electron. Trans. Numer. Anal., 49.
S. 244 - 274.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395, Rheinbach, Oliver
ORCID: 0000-0002-9310-8533 and Uran, Matthias
(2017).
NONLINEAR FETI-DP AND BDDC METHODS: A UNIFIED FRAMEWORK AND PARALLEL RESULTS.
SIAM J. Sci. Comput., 39 (6).
S. C417 - 35.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Klawonn, Axel ORCID: 0000-0003-4765-7387, Kuehn, Martin and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2016).
ADAPTIVE COARSE SPACES FOR FETI-DP IN THREE DIMENSIONS.
SIAM J. Sci. Comput., 38 (5).
S. A2880 - 32.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Klawonn, Axel ORCID: 0000-0003-4765-7387, Radtke, Patrick and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2016).
A COMPARISON OF ADAPTIVE COARSE SPACES FOR ITERATIVE SUBSTRUCTURING IN TWO DIMENSIONS.
Electron. Trans. Numer. Anal., 45.
S. 75 - 107.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Balzani, Daniel ORCID: 0000-0002-1422-4262, Deparis, Simone
ORCID: 0000-0002-2832-6630, Fausten, Simon, Forti, Davide, Heinlein, Alexander
ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Quarteroni, Alfio, Rheinbach, Oliver
ORCID: 0000-0002-9310-8533 and Schroeder, Joerg
(2016).
Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.
Int. J. Numer. Meth. Biomed., 32 (10).
HOBOKEN:
WILEY.
ISSN 2040-7947
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387 and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2016).
A PARALLEL IMPLEMENTATION OF A TWO-LEVEL OVERLAPPING SCHWARZ METHOD WITH ENERGY-MINIMIZING COARSE SPACE BASED ON TRILINOS.
SIAM J. Sci. Comput., 38 (6).
S. C713 - 35.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2015).
TOWARD EXTREMELY SCALABLE NONLINEAR DOMAIN DECOMPOSITION METHODS FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS.
SIAM J. Sci. Comput., 37 (6).
S. C667 - 30.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Hetmaniuk, Ulrich and Klawonn, Axel ORCID: 0000-0003-4765-7387
(2014).
ERROR ESTIMATES FOR A TWO-DIMENSIONAL SPECIAL FINITE ELEMENT METHOD BASED ON COMPONENT MODE SYNTHESIS.
Electron. Trans. Numer. Anal., 41.
S. 109 - 133.
KENT:
KENT STATE UNIVERSITY.
ISSN 1068-9613
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Rheinbach, Oliver
ORCID: 0000-0002-9310-8533
(2014).
NONLINEAR FETI-DP AND BDDC METHODS.
SIAM J. Sci. Comput., 36 (2).
S. A737 - 29.
PHILADELPHIA:
SIAM PUBLICATIONS.
ISSN 1095-7197
Preprints, Working Papers or Reports
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2024).
Reduced Dimension GDSW Coarse Spaces for Monolithic Schwarz Domain Decomposition Methods for Incompressible Fluid Flow Problems (CDS-2019-12 – Version 2).
Technical Report.
Grimm, Viktor ORCID: 0000-0001-5300-3705, Heinlein, Alexander
ORCID: 0000-0003-1578-8104 and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2022).
A short note on solving partial differential equations using convolutional neural networks.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387 and Lanser, Martin
ORCID: 0000-0002-4232-9395
(2022).
Efficient Adaptive Elimination Strategies in Nonlinear FETI-DP Methods in Combination with Adaptive Spectral Coarse Spaces.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Wasiak, Adam
ORCID: 0000-0002-5705-9754
(2022).
Three-level BDDC for Virtual Elements.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Weber, Janine
ORCID: 0000-0002-6692-2230
(2022).
Adaptive Three-level BDDC Using Frugal Constraints.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Weber, Janine
ORCID: 0000-0002-6692-2230
(2022).
Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Weber, Janine
ORCID: 0000-0002-6692-2230
(2022).
Learning Adaptive Coarse Basis Functions of FETI-DP.
Technical Report.
Balzani, Daniel ORCID: 0000-0002-1422-4262, Heinlein, Alexander
ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Rheinbach, Oliver
ORCID: 0000-0002-9310-8533 and Schröder, Jörg
(2022).
Comparison of Arterial Wall Models in Fluid-Structure Interaction Simulations.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin
ORCID: 0000-0002-4232-9395 and Wasiak, Adam
(2021).
Adaptive and Frugal FETI-DP for Virtual Elements.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387 and Lanser, Martin
ORCID: 0000-0002-4232-9395
(2021).
Adaptive Nonlinear Domain Decomposition Methods.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver
ORCID: 0000-0002-9310-8533 and Uran, Matthias
(2021).
Fully-Coupled Micro-Macro Finite Element Simulations of the Nakajima Test Using Parallel Computational Homogenization.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Uran, Matthias
(2021).
Adaptive Nonlinear Elimination in Nonlinear FETI-DP Methods.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2021).
Predicting the geometric location of critical edges in adaptive GDSW overlapping domain decomposition methods using deep learning.
Technical Report.
Eichinger, Matthias, Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2020).
Surrogate Convolutional Neural Network Models for Steady Computational Fluid Dynamics Simulations.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2020).
Combining Machine Learning and Domain Decomposition Methods – A Review.
Technical Report.
Grimm, Viktor, Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2020).
Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Knepper, Jascha
ORCID: 0000-0002-8769-2235, Rheinbach, Oliver and Widlund, Olof B.
(2020).
Adaptive GDSW coarse spaces of reduced dimension for overlapping Schwarz methods.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2020).
Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2019).
Fully algebraic two-level overlapping Schwarz preconditioners for elasticity problems.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2019).
Machine Learning in Adaptive FETI-DP - Reducing the Effort in Sampling.
Technical Report.
Eichinger, Matthias, Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2019).
Stationary flow predictions using convolutional neural networks.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Klawonn, Axel
ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2019).
A Frugal FETI-DP and BDDC Coarse Space for Heterogeneous Problems.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver and Weber, Janine
(2019).
Preconditioning the coarse problem of BDDC methods - Three-level, algebraic multigrid, and vertex-based preconditioners.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel
ORCID: 0000-0003-4765-7387
(2019).
Reduced Dimension GDSW Coarse Spaces for Monolithic Schwarz Domain Decomposition Methods for Incompressible Fluid Flow Problems.
Technical Report.
Giese, Daniel, Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha
ORCID: 0000-0002-8769-2235 and Peters, Kristina
ORCID: 0000-0003-3064-0247
(2019).
Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - A benchmark problem.
Technical Report.
Giese, Daniel, Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha
ORCID: 0000-0002-8769-2235 and Peters, Kristina
ORCID: 0000-0003-3064-0247
(2019).
Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - Influence of noisy MRI measurements.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Köhler, Stephan, Lanser, Martin and Rheinbach, Oliver
(2019).
Computational Homogenization with Million-way Parallelism using Domain Decomposition Methods.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Kühn, Martin Joachim
ORCID: 0000-0002-0906-6984 and Rheinbach, Oliver
(2019).
Parallel adaptive FETI-DP using lightweight asynchronous dynamic load balancing.
Technical Report.
Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Rajamanickam, Sivasankaran and Rheinbach, Oliver
(2018).
FROSch: A Fast And Robust Overlapping Schwarz Domain Decomposition Preconditioner Based on Xpetra in Trilinos.
Technical Report.
Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387 and Kühn, Martin Joachim
ORCID: 0000-0002-0906-6984
(2018).
Local spectra of adaptive domain decomposition methods.
Technical Report.
Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin and Weber, Janine
(2018).
Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data.
Technical Report.
Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Rheinbach, Oliver and Röver, Friederike
(2018).
A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Three Dimensions.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Kühn, Martin Joachim
ORCID: 0000-0002-0906-6984 and Rheinbach, Oliver
(2018).
A closer look at local eigenvalue solvers for adaptive FETI-DP and BDDC.
Technical Report.
Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Knepper, Jascha
ORCID: 0000-0002-8769-2235 and Rheinbach, Oliver
(2018).
Adaptive GDSW coarse spaces for overlapping Schwarz methods in three dimensions.
Technical Report.
Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin Heinrich, Rheinbach, Oliver, Wellein, Gerhard and Wittmann, Markus
(2018).
Energy Efficiency of Nonlinear Domain Decomposition Methods.
Technical Report.
Heinlein, Alexander, Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin Heinrich and Weber, Janine
(2018).
Machine Learning in adaptive domain decomposition methods - predicting the geometric location of constraints.
Technical Report.
Heinlein, Alexander, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387
(2018).
Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Saddle Point Problems.
Technical Report.