Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic materials
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911424431783936 |
|---|---|
| author | Firmbach, Max Phillips, Malachi Glusa, Christian Popp, Alexander Siefert, Christopher M. Mayr, Matthias |
| author_facet | Firmbach, Max Phillips, Malachi Glusa, Christian Popp, Alexander Siefert, Christopher M. Mayr, Matthias |
| contents | This paper introduces a material-aware strength-of-connection measure for smoothed aggregation algebraic multigrid methods, aimed at improving robustness for scalar partial differential equations with heterogeneous and anisotropic material properties. Classical strength-of-connection measures typically rely only on matrix entries or geometric distances, which often fail to capture weak couplings across material interfaces or align with anisotropy directions, ultimately leading to poor convergence. The proposed approach directly incorporates material tensor information into the coarsening process, enabling a reliable detection of weak connections and ensuring that coarse levels preserve the true structure of the underlying problem. As a result, smooth error components are represented properly and sharp coefficient jumps or directional anisotropies are handled consistently. A wide range of academic tests and real-world applications, including thermally activated batteries and solar cells, demonstrate that the proposed method maintains robustness across material contrasts, anisotropies, and mesh variations. Scalability and parallel performance of the algebraic multigrid method highlight the suitability for large-scale, high-performance computing environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05686 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic materials Firmbach, Max Phillips, Malachi Glusa, Christian Popp, Alexander Siefert, Christopher M. Mayr, Matthias Computational Engineering, Finance, and Science Distributed, Parallel, and Cluster Computing This paper introduces a material-aware strength-of-connection measure for smoothed aggregation algebraic multigrid methods, aimed at improving robustness for scalar partial differential equations with heterogeneous and anisotropic material properties. Classical strength-of-connection measures typically rely only on matrix entries or geometric distances, which often fail to capture weak couplings across material interfaces or align with anisotropy directions, ultimately leading to poor convergence. The proposed approach directly incorporates material tensor information into the coarsening process, enabling a reliable detection of weak connections and ensuring that coarse levels preserve the true structure of the underlying problem. As a result, smooth error components are represented properly and sharp coefficient jumps or directional anisotropies are handled consistently. A wide range of academic tests and real-world applications, including thermally activated batteries and solar cells, demonstrate that the proposed method maintains robustness across material contrasts, anisotropies, and mesh variations. Scalability and parallel performance of the algebraic multigrid method highlight the suitability for large-scale, high-performance computing environments. |
| title | Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic materials |
| topic | Computational Engineering, Finance, and Science Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2602.05686 |