Two-Level Preconditioners for the Helmholtz Equation

DOI10.1007/978-3-319-93873-8_11zbMath1443.65416arXiv1705.08139OpenAlexW2617610143MaRDI QIDQ5114531

Victorita Dolean, Pierre-Henri Tournier, Marcella Bonazzoli, Ivan G. Graham, Euan A. Spence

Publication date: 24 June 2020

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

Full work available at URL: https://arxiv.org/abs/1705.08139

zbMATH Keywords

preconditioningGMRESHelmholtz equationDirichlet-to-Neumann mapstwo-level preconditionerslocal eigenproblems

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Preconditioners for iterative methods (65F08)

Related Items (9)

Schwarz methods by domain truncation ⋮ Substructured two-grid and multi-grid domain decomposition methods ⋮ A coercive heterogeneous media Helmholtz model: formulation, wavenumber-explicit analysis, and preconditioned high-order FEM ⋮ Domain Decomposition with Local Impedance Conditions for the Helmholtz Equation with Absorption ⋮ Multilevel Optimized Schwarz Methods ⋮ A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics ⋮ A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems ⋮ Towards accuracy and scalability: combining isogeometric analysis with deflation to obtain scalable convergence for the Helmholtz equation ⋮ Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

Cites Work

• Restricted overlapping balancing domain decomposition methods and restricted coarse problems for the Helmholtz problem
• A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator
• Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption
• Recent Results on Domain Decomposition Preconditioning for the High-Frequency Helmholtz Equation Using Absorption

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