An adaptive mesh refinement scheme for hierarchical hybrid grids

Mann B, Rüde U (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Applications of Mathematics Springer Verlag (Germany) / Akademie věd České republiky, Matematický ústav

Book Volume: 70

Pages Range: 875-905

Journal Issue: 6

DOI: 10.21136/AM.2025.0186-25

Abstract

This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block-structured hierarchical hybrid grids, this is accomplished by using classical, unstructured refinement only on the coarsest level of the hierarchy, while keeping the number of structured refinement levels constant over the whole domain. This leads to a compromise, where the excellent performance characteristics of hierarchical hybrid grids can be maintained at the price that the flexibility of generating locally refined meshes is constrained. Furthermore, the mesh adaptivity often relies on a posteriori error estimators or error indicators, which tend to become computationally expensive. Again, with the goal of preserving scalability and performance, a method is proposed that leverages the grid hierarchy and the full multigrid scheme. Utilizing the sequence of approximations on the nested hierarchy of grids permits the computation of a cheap error estimator that is well-suited for large-scale parallel computing. We present the theoretical foundations for both global and local error estimates, and present a rigorous analysis of their effectivity. The proposed method, including the error estimator and the adaptive coarse grid refinement, is implemented in the finite element framework HyTeG. Extensive numerical experiments are conducted to validate the effectiveness, as well as performance and scalability.

Authors with CRIS profile

Benjamin Mann Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)

Involved external institutions

Technical University of Ostrava / Vysoká škola báňská - Technická univerzita Ostrava CZ Czech Republic (CZ)

How to cite

APA:

Mann, B., & Rüde, U. (2025). An adaptive mesh refinement scheme for hierarchical hybrid grids. Applications of Mathematics, 70(6), 875-905. https://doi.org/10.21136/AM.2025.0186-25

MLA:

Mann, Benjamin, and Ulrich Rüde. "An adaptive mesh refinement scheme for hierarchical hybrid grids." Applications of Mathematics 70.6 (2025): 875-905.

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