publications

Alexander Heinlein's publications in reversed chronological order.

Journal Articles

2024

  1. CMAME
    Multilevel domain decomposition-based architectures for physics-informed neural networks
    Victorita DoleanAlexander HeinleinSiddhartha Mishra, and 1 more author
    Computer Methods in Applied Mechanics and Engineering, 2024
  2. GAMM-Mitteilungen
    A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods
    Daniel BalzaniAlexander HeinleinAxel Klawonn, and 5 more authors
    GAMM-Mitteilungen, 2024

2023

  1. Ocean Engineering
    Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data
    Svenja Ehlers, Marco Klein, Alexander Heinlein, and 4 more authors
    Ocean Engineering, 2023
  2. JCOMP
    Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth
    Stefan Frei, and Alexander Heinlein
    Journal of Computational Physics, 2023
  3. CMAM
    A Multi-Level Extension of the GDSW Overlapping Schwarz Preconditioner
    Alexander HeinleinOliver Rheinbach, and Friederike Röver
    Computational Methods in Applied Mathematics, 2023
  4. CM
    Comparison of Arterial Wall Models in Fluid-Structure Interaction Simulations
    Daniel BalzaniAlexander HeinleinAxel Klawonn, and 2 more authors
    Computational Mechanics, 2023

2022

  1. SISC
    Parallel Scalability of Three-Level FROSch Preconditioners to 220 000 Cores using the Theta Supercomputer
    Alexander HeinleinOliver Rheinbach, and Friederike Röver
    SIAM Journal on Scientific Computing, 2022
  2. SISC
    Adaptive nonlinear domain decomposition methods with an application to the p-Laplacian
    Alexander HeinleinAxel Klawonn, and Martin Lanser
    SIAM Journal on Scientific Computing, 2022
  3. MRS Advances
    Irradiation-dependent Topology Optimization of Metallization Grid Patterns and Variation of Contact Layer Thickness used for Latitude-based Yield Gain of Thin-film Solar Modules
    Mario Zinßer, Benedikt Braun, Tim Helder, and 6 more authors
    MRS Advances, 2022
  4. SISC
    Adaptive GDSW Coarse Spaces of Reduced Dimension for Overlapping Schwarz Methods
    Alexander HeinleinAxel KlawonnJascha Knepper, and 2 more authors
    SIAM Journal on Scientific Computing, 2022
  5. SISC
    FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica
    Alexander HeinleinMauro Perego, and Sivasankaran Rajamanickam
    SIAM Journal on Scientific Computing, 2022
  6. ETNA
    Surrogate convolutional neural network models for steady computational fluid dynamics simulations
    Matthias Eichinger, Alexander Heinlein, and Axel Klawonn
    Electronic Transactions on Numerical Analysis (ETNA), 2022
  7. ETNA
    Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks
    Viktor GrimmAlexander HeinleinAxel Klawonn, and 2 more authors
    Electronic Transactions on Numerical Analysis (ETNA), 2022

2021

  1. SISC
    Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions
    Alexander HeinleinAxel KlawonnMartin Lanser, and 1 more author
    SIAM Journal on Scientific Computing, 2021
  2. GAMM-Mitteilungen
    Combining Machine Learning and Domain Decomposition Methods for the Solution of Partial Differential Equations – A Review
    Alexander HeinleinAxel KlawonnMartin Lanser, and 1 more author
    GAMM-Mitteilungen, 2021

2020

  1. ETNA
    A Frugal FETI-DP and BDDC Coarse Space for Heterogeneous Problems
    Alexander HeinleinAxel KlawonnMartin Lanser, and 1 more author
    Electronic Transactions on Numerical Analysis (ETNA), 2020
  2. SISC
    Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids
    Alexander Heinlein, and Martin Lanser
    SIAM Journal on Scientific Computing, 2020
  3. IJNME
    Reduced Dimension GDSW Coarse Spaces for Monolithic Schwarz Domain Decomposition Methods for Incompressible Fluid Flow Problems
    Alexander HeinleinChristian Hochmuth, and Axel Klawonn
    International Journal for Numerical Methods in Engineering, 2020

2019

  1. SISC
    Machine Learning in Adaptive Domain Decomposition Methods - Predicting the Geometric Location of Constraints
    Alexander HeinleinAxel KlawonnMartin Lanser, and 1 more author
    SIAM Journal on Scientific Computing, 2019
  2. SISC
    Adaptive GDSW Coarse Spaces for Overlapping Schwarz Methods in Three Dimensions
    Alexander HeinleinAxel KlawonnJascha Knepper, and 1 more author
    SIAM Journal on Scientific Computing, 2019
  3. SISC
    Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Incompressible Fluid Flow Problems
    Alexander HeinleinChristian Hochmuth, and Axel Klawonn
    SIAM Journal on Scientific Computing, 2019

2018

  1. ETNA
    Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2D
    Alexander HeinleinAxel KlawonnJascha Knepper, and 1 more author
    Electronic Transactions on Numerical Analysis (ETNA), 2018

2016

  1. SISC
    A parallel implementation of a two-level overlapping Schwarz method with energy-minimizing coarse space based on Trilinos
    Alexander HeinleinAxel Klawonn, and Oliver Rheinbach
    SIAM Journal on Scientific Computing, 2016
  2. IJNMBE
    Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains
    Daniel BalzaniSimone Deparis, Simon Fausten, and 6 more authors
    International Journal for Numerical Methods in Biomedical Engineering, 2016

2015

  1. JCAM
    The approximate component mode synthesis special finite element method in two dimensions: Parallel implementation and numerical results
    Alexander Heinlein, Ulrich Hetmaniuk, Axel Klawonn, and 1 more author
    Journal of Computational and Applied Mathematics, 2015
    Sixth International Conference on Advanced Computational Methods in Engineering (ACOMEN 2014)

Conference Proceedings

2024

  1. Springer LNCSE
    A short note on solving partial differential equations using convolutional neural networks
    Viktor GrimmAlexander Heinlein, and Axel Klawonn
    In Domain Decomposition Methods in Science and Engineering XXVII, 2024
  2. Springer LNCSE
    Finite basis physics-informed neural networks as a Schwarz domain decomposition method
    Victorita DoleanAlexander HeinleinSiddhartha Mishra, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXVII, 2024

2023

  1. Coupled2023
    A Comparison Of Direct Solvers In FROSch Applied To Chemo-Mechanics
    Alexander Heinlein, Björn Kiefer, Stefan Prüger, and 2 more authors
    In 10th edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering, 2023
  2. IPDPS
    An Experimental Study of Two-level Schwarz Domain-Decomposition Preconditioners on GPUs
    Ichitaro Yamazaki, Alexander Heinlein, and Sivasankaran Rajamanickam
    In 2023 IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2023
  3. PAMM
    Reduced order fluid modeling with generative adversarial networks
    Mirko Kemna, Alexander Heinlein, and Cornelis Vuik
    In Proc. Appl. Math. Mech., 2023
  4. PAMM
    First steps towards modeling the interaction of cardiovascular agents and smooth muscle activation in arterial walls
    Sharan Nurani Ramesh, Klemens UhlmannLea Saßmannshausen, and 4 more authors
    In Proc. Appl. Math. Mech., 2023
  5. Springer LNCSE
    A Three-Level Extension for Fast and Robust Overlapping Schwarz (FROSch) Preconditioners with Reduced Dimensional Coarse Space
    Alexander HeinleinAxel KlawonnOliver Rheinbach, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXVI, 2023
  6. Springer LNCSE
    Predicting the geometric location of critical edges in adaptive GDSW overlapping domain decomposition methods using deep learning
    Alexander HeinleinAxel KlawonnMartin Lanser, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXVI, 2023

2022

  1. WCCM-ECCOMAS
    Efficient coarse correction for parallel time-stepping in plaque growth simulations
    Stefan Frei, and Alexander Heinlein
    In ECCOMAS2022, 2022

2021

  1. PAMM
    On temporal homogenization in the numerical simulation of atherosclerotic plaque growth
    Stefan FreiAlexander Heinlein, and Thomas Richter
    In Proc. Appl. Math. Mech., 2021
  2. Springer LNCSE
    Stationary flow predictions using convolutional neural networks
    Matthias Eichinger, Alexander Heinlein, and Axel Klawonn
    In Numerical Mathematics and Advanced Applications ENUMATH 2019, 2021
  3. Springer LNCSE
    Fully algebraic two-level overlapping Schwarz preconditioners for elasticity problems
    Alexander HeinleinChristian Hochmuth, and Axel Klawonn
    In Numerical Mathematics and Advanced Applications ENUMATH 2019, 2021
  4. Springer LNCSE
    Machine Learning in Adaptive Domain Decomposition Methods - Reducing the Effort in Sampling
    Alexander HeinleinAxel KlawonnMartin Lanser, and 1 more author
    In Numerical Mathematics and Advanced Applications ENUMATH 2019, 2021
  5. WCCM-ECCOMAS
    Choosing the Subregions in Three-Level FROSch Preconditioners
    Alexander HeinleinOliver Rheinbach, and Friederike Röver
    In WCCM-ECCOMAS2020, 2021

2020

  1. Springer LNCSE
    Coarse Spaces for Nonlinear Schwarz Methods on Unstructured Grids
    Alexander Heinlein, and Martin Lanser
    In Domain Decomposition Methods in Science and Engineering XXV, 2020
  2. Springer LNCSE
    Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data
    Alexander HeinleinAxel KlawonnMartin Lanser, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXV, 2020
  3. Springer LNCSE
    Local spectra of adaptive domain decomposition methods
    Alexander HeinleinAxel Klawonn, and Martin Kühn
    In Domain Decomposition Methods in Science and Engineering XXV, 2020
  4. Springer LNCSE
    FROSch: A Fast And Robust Overlapping Schwarz Domain Decomposition Preconditioner Based on Xpetra in Trilinos
    Alexander HeinleinAxel KlawonnSivasankaran Rajamanickam, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXV, 2020
  5. Springer LNCSE
    A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Three Dimensions
    Alexander HeinleinAxel KlawonnOliver Rheinbach, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXV, 2020

2019

  1. Springer LNCSE
    A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions
    Alexander HeinleinAxel KlawonnOliver Rheinbach, and 1 more author
    In Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017, 2019
  2. Springer LNCSE
    Improving the Parallel Performance of Overlapping Schwarz Methods by Using a Smaller Energy Minimizing Coarse Space
    Alexander HeinleinAxel KlawonnOliver Rheinbach, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXIV, 2019
  3. Springer LNCSE
    An Adaptive GDSW Coarse Space for Two-Level Overlapping Schwarz Methods in Two Dimensions
    Alexander HeinleinAxel KlawonnJascha Knepper, and 1 more author
    In Domain Decomposition Methods in Science and Engineering XXIV, 2019
  4. PAMM
    Applying the FROSch Overlapping Schwarz Preconditioner to Dislocation Mechanics in Deal.II
    Alexander HeinleinOliver RheinbachFriederike Röver, and 2 more authors
    In Proc. Appl. Math. Mech., 2019
  5. PAMM
    Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - A benchmark problem
    Daniel Giese, Alexander HeinleinAxel Klawonn, and 2 more authors
    In Proc. Appl. Math. Mech., 2019
  6. PAMM
    Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model - Influence of noisy MRI measurements
    Daniel Giese, Alexander HeinleinAxel Klawonn, and 2 more authors
    In Proc. Appl. Math. Mech., 2019

2018

  1. PAMM
    Remarks on Fluid-Structure Interaction Simulations in Realistic Arterial Geometries with regard to the Transmural Stress Distribution
    Simon Fausten, Daniel BalzaniAlexander Heinlein, and 3 more authors
    In Proc. Appl. Math. Mech., 2018

2017

  1. Springer LNCSE
    Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space
    Alexander HeinleinAxel Klawonn, and Oliver Rheinbach
    In Domain Decomposition Methods in Science and Engineering XXIII, 2017
  2. PAMM
    Steps Towards More Realistic FSI Simulations of Coronary Arteries
    Simon Fausten, Daniel BalzaniAlexander Heinlein, and 3 more authors
    In Proc. Appl. Math. Mech., 2017

2016

  1. Springer LNCSE
    Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction
    Alexander HeinleinAxel Klawonn, and Oliver Rheinbach
    In Numerical Mathematics and Advanced Applications ENUMATH 2015, 2016

2015

  1. PAMM
    A Comparison of Preconditioners for the Steklov–Poincaré Formulation of the Fluid-Structure Coupling in Hemodynamics
    Simone Deparis, Davide Forti, Alexander Heinlein, and 3 more authors
    In Proc. Appl. Math. Mech., 2015

2014

  1. WCCM XI
    Aspects of Arterial Wall Simulations: Nonlinear Anisotropic Material Models and Fluid Structure Interaction
    Daniel BalzaniSimone Deparis, Simon Fausten, and 6 more authors
    In Proceedings of the WCCM XI, 2014

Theses

2016

  1. PhD Thesis
    Parallel Overlapping Schwarz Preconditioners and Multiscale Discretizations with Applications to Fluid-Structure Interaction and Highly Heterogeneous Problems
    Alexander Heinlein
    Universität zu Köln, 2016

Technical Reports

2024

  1. Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems
    Alexander HeinleinAmanda A. HowardDamien Beecroft, and 1 more author
    Jan 2024
    Accepted for publication
  2. Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks
    Anouk Zandbergen, Tycho van Noorden, and Alexander Heinlein
    Jun 2024
    Submitted

2023

  1. A fully algebraic and robust two-level Schwarz method based on optimal local approximation spaces
    Alexander Heinlein, and Kathrin Smetana
    Aug 2023
    Submitted
  2. Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks
    Viktor GrimmAlexander Heinlein, and Axel Klawonn
    Aug 2023
    Submitted
  3. An extension of the approximate component mode synthesis method to the heterogeneous Helmholtz equation
    Elena GiammatteoAlexander Heinlein, and Matthias Schlottbom
    Oct 2023
    Submitted