ALGEBRAIC MULTIGRID METHODS FOR METRIC-PERTURBED COUPLED PROBLEMS

Ana Budiša, Xiaozhe Hu, Miroslav Kuchta, Kent Andre Mardal, Ludmil Zikatanov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on aggregation-based algebraic multigrid methods with custom smoothers that preserve the coupling information on each coarse level. We prove that, with the proper choice of subspace splitting, we obtain uniform convergence in discretization and physical parameters in the two-level setting. Additionally, we show parameter robustness and scalability with regard to the number of the degrees of freedom of the system on several numerical examples related to the biophysical processes in the brain, namely, the electric signaling in excitable tissue modeled by bidomain, the extracellular-membrane-intracellular (EMI) model, and reduced EMI equations.

Original languageEnglish (US)
Pages (from-to)A1461-A1486
JournalSIAM Journal on Scientific Computing
Volume46
Issue number3
DOIs
StatePublished - Jun 2024

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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