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PreprintarXiv licencearXiv

Semi-Algebraic Mode Analysis For Finite Element Discretisations Of The Heat Equation

  • A. Mesforush
  • N. Habibi
  • F. Gasper
  • C. Rodrigo
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Abstract

In this work, a semialgebraic mode analysis (SAMA) is proposed for investigating the convergence of a multigrid waveform relaxation method applied to the Finite Element (FE) discretization of the heat equation in two and three dimensions. This analysis for finite element methods is more involved and more general than that for Finite Difference (FD) discretizations, since mass matrix must be considered. The proposed analysis results in a very useful tool to study the behaviour of the multigrid waveform relaxation method depending on the parameters of the problem.

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Cite

BibTeXRIS
BibTeX
@misc{mesforush2026semialgebraic,
  title = {{Semi-Algebraic Mode Analysis For Finite Element Discretisations Of The Heat Equation}},
  author = {A. Mesforush and N. Habibi and F. Gasper and C. Rodrigo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27934},
  eprint = {2609.27934},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27934},
}
RIS
TY  - UNPB
TI  - Semi-Algebraic Mode Analysis For Finite Element Discretisations Of The Heat Equation
AU  - A. Mesforush
AU  - N. Habibi
AU  - F. Gasper
AU  - C. Rodrigo
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.27934
UR  - https://arxiv.org/abs/2609.27934
AB  - In this work, a semialgebraic mode analysis (SAMA) is proposed for investigating the convergence of a multigrid waveform relaxation method applied to the Finite Element (FE) discretization of the heat equation in two and three dimensions. This analysis for finite element methods is more involved and more general than that for Finite Difference (FD) discretizations, since mass matrix must be considered. The proposed analysis results in a very useful tool to study the behaviour of the multigrid waveform relaxation method depending on the parameters of the problem.
ER  -