Alexander Heinlein

recent publications (full list)

1. PAMM

   On temporal homogenization in the numerical simulation of atherosclerotic plaque growth

   Frei, Stefan, Heinlein, Alexander, and Richter, Thomas

   In PAMM 2021

   Abstract Bib doi HTML Preprint

   A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields significantly different results compared to a simple heuristic averaging, where only stationary long-scale FSI problems are solved, confirming the importance of incorporating stress variations on small time-scales. In the homogenization approach, a periodic fine-scale problem, which is periodic with respect to the heart beat, has to be solved for each long-scale time step. Even if no exact initial conditions are available, periodicity can be achieved within only 2–3 heart beats by simple time-stepping.

   @inproceedings{Frei:2021:THN,
     author = {Frei, Stefan and Heinlein, Alexander and Richter, Thomas},
     title = {On temporal homogenization in the numerical simulation of atherosclerotic plaque growth},
     booktitle = {PAMM},
     volume = {21},
     number = {1},
     pages = {e202100055},
     year = {2021},
     doi = {10.1002/pamm.202100055},
     abbr = {PAMM},
     url = {https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100055},
     preprint = {https://arxiv.org/abs/2106.09394},
     keywords = {published, recent},
     bibtex_show = {true}
   }

2. SISC

   FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

   Heinlein, Alexander, Perego, Mauro, and Rajamanickam, Sivasankaran

   Accepted for publication in SIAM Journal on Scientific Computing. January 2022

   Abstract Bib Preprint

   Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level GDSW (Generalized Dryja-Smith-Widlund) type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the MPI-parallel implementation of multi-level Schwarz preconditioners provided by the package FROSch (Fast and Robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To our knowledge, this is the first time two-level Schwarz preconditioners are applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as non uniform meshes for the Greenland ice sheet are considered. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32 K processor cores (8 K MPI-ranks and 4 OpenMP threads) and 566 M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4 K processor cores (and MPI-ranks) and 68 M degrees of freedom for the coupled problem.

   @techreport{Heinlein:2022:FRO,
     author = {Heinlein, Alexander and Perego, Mauro and Rajamanickam, Sivasankaran},
     title = {FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica},
     note = {Accepted for publication in SIAM Journal on Scientific Computing. January 2022},
     abbr = {SISC},
     preprint = {https://kups.ub.uni-koeln.de/id/eprint/30668},
     keywords = {accepted, reviewed, selected, recent},
     bibtex_show = {true}
   }

3. ETNA

   Surrogate Convolutional Neural Network Models for Steady Computational Fluid Dynamics Simulations

   Eichinger, Matthias, Heinlein, Alexander, and Klawonn, Axel

   Accepted for publication in ETNA. October 2021.

   Abstract Bib Preprint

   A convolution neural network (CNN)-based approach for the construction of reduced order surrogate models for computational fluid dynamics (CFD) simulations is introduced; it is inspired by the approach of Guo, Li, and Iori [X. Guo, W. Li, and F. Iorio, Convolutional neural networks for steady flow approximation, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD’16, New York, USA, 2016, ACM, pp. 481–490]. In particular, the neural networks are trained in order to predict images of the flow field in a channel with varying obstacle based on an image of the geometry of the channel. A classical CNN with bottleneck structure and a U-Net are compared while varying the input format, the number of decoder paths, as well as the loss function used to train the networks. This approach yields very low prediction errors, in particular, when using the U-Net architecture. Furthermore, the models are also able to generalize to unseen geometries of the same type. A transfer learning approach enables the model to be trained to a new type of geometries with very low training cost. Finally, based on this transfer learning approach, a sequential learning strategy is introduced, which significantly reduces the amount of necessary training data.

   @techreport{Eichinger:2021:SCN,
     author = {Eichinger, Matthias and Heinlein, Alexander and Klawonn, Axel},
     title = {Surrogate Convolutional Neural Network Models for Steady Computational Fluid Dynamics Simulations},
     note = {Accepted for publication in ETNA. October 2021.},
     abbr = {ETNA},
     preprint = {https://kups.ub.uni-koeln.de/29760/},
     keywords = {accepted, reviewed, selected, recent},
     bibtex_show = {true}
   }

4. SISC

   Adaptive GDSW coarse spaces of reduced dimension for overlapping Schwarz methods

   Heinlein, Alexander, Klawonn, Axel, Knepper, Jascha, Rheinbach, Oliver, and Widlund, Olof B.

   Accepted for publication in SIAM Journal on Scientific Computing. October 2021

   Abstract Bib Preprint

   A new reduced dimension adaptive GDSW (Generalized Dryja-Smith-Widlund) overlapping Schwarz method for linear second-order elliptic problems in three dimensions is introduced. It is robust with respect to large contrasts of the coefficients of the partial differential equations. The condition number bound of the new method is shown to be independent of the coefficient contrast and only dependent on a user-prescribed tolerance. The interface of the nonoverlapping domain decomposition is partitioned into nonoverlapping patches. The new coarse space is obtained by selecting a few eigenvectors of certain local eigenproblems which are defined on these patches. These eigenmodes are energy-minimally extended to the interior of the nonoverlapping subdomains and added to the coarse space. By using a new interface decomposition the reduced dimension adaptive GDSW overlapping Schwarz method usually has a smaller coarse space than existing GDSW and adaptive GDSW domain decomposition methods. A robust condition number estimate is proven for the new reduced dimension adaptive GDSW method which is also valid for existing adaptive GDSW methods. Numerical results for the equations of isotropic linear elasticity in three dimensions confirming the theoretical findings are presented.

   @techreport{Heinlein:2021:AGD,
     author = {Heinlein, Alexander and Klawonn, Axel and Knepper, Jascha and Rheinbach, Oliver and Widlund, Olof B.},
     title = {Adaptive GDSW coarse spaces of reduced dimension for overlapping Schwarz methods},
     note = {Accepted for publication in SIAM Journal on Scientific Computing. October 2021},
     abbr = {SISC},
     preprint = {https://kups.ub.uni-koeln.de/id/eprint/12113},
     keywords = {accepted, reviewed, recent},
     bibtex_show = {true}
   }