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Journal Article
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
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 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
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
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
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.
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.
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.
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.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Perego, Mauro and Rajamanickam, Sivasankaran
(2021).
FROSch Preconditioners for Land Ice Simulations of
Greenland and Antarctica.
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.
Heinlein, Alexander ORCID: 0000-0003-1578-8104 and Lanser, Martin
(2019).
Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids.
Technical Report.
Heinlein, Alexander ORCID: 0000-0003-1578-8104, Rheinbach, Oliver, Röver, Friederike, Sandfeld, Stefan and Steinberger, Dominik
(2019).
Applying the FROSch Overlapping Schwarz Preconditioner for Dislocation Mechanics in Deal.II.
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.