On the Dirichlet-to-Neumann Coarse Space for Solving the Helmholtz Problem Using Domain Decomposition

DOI10.1007/978-3-030-55874-1_16zbMath1470.65204arXiv1912.06053OpenAlexW3164223535MaRDI QIDQ5152804

Niall Bootland, Victorita Dolean

Publication date: 27 September 2021

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.06053

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical methods for partial differential equations, boundary value problems (65N99)

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Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices, A comparison of coarse spaces for Helmholtz problems in the high frequency regime

Cites Work

• Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps
• A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• A Coarse Space Construction Based on Local Dirichlet-to-Neumann Maps
• An Introduction to Domain Decomposition Methods
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?