Additive Sweeping Preconditioner for the Helmholtz Equation

DOI10.1137/15M1017144zbMath1338.65077arXiv1504.04058MaRDI QIDQ2806427

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Publication date: 18 May 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.04058

zbMATH Keywords

Helmholtz equationpreconditionersperfectly matched layershigh frequency waves

Mathematics Subject Classification ID

Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (12)

Reduced basis stochastic Galerkin methods for partial differential equations with random inputs ⋮ An adaptive ANOVA stochastic Galerkin method for partial differential equations with high-dimensional random inputs ⋮ Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media ⋮ Sparsify and Sweep: An Efficient Preconditioner for the Lippmann--Schwinger Equation ⋮ An Additive Overlapping Domain Decomposition Method for the Helmholtz Equation ⋮ A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods ⋮ Double Source Transfer Domain Decomposition Method For Helmholtz Problems ⋮ Fast Alternating BiDirectional Preconditioner for the 2D High-Frequency Lippmann--Schwinger Equation ⋮ Optimal Complex Relaxation Parameters in Multigrid for Complex-Shifted Linear Systems ⋮ A pure source transfer domain decomposition method for Helmholtz equations in unbounded domain ⋮ Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems ⋮ A Rational Function Preconditioner For Indefinite Sparse Linear Systems

Uses Software

• PSP
• clique
• AILU

Cites Work

• A rapidly converging domain decomposition method for the Helmholtz equation
• Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
• A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements
• A sweeping preconditioner for Yee's finite difference approximation of time-harmonic Maxwell's equations
• The method of polarized traces for the 2D Helmholtz equation
• Advances in iterative methods and preconditioners for the Helmholtz equation
• A perfectly matched layer for the absorption of electromagnetic waves
• Recursive Sweeping Preconditioner for the Three-Dimensional Helmholtz Equation
• A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
• A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain
• Sweeping preconditioners for elastic wave propagation with spectral element methods
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• AILU FOR HELMHOLTZ PROBLEMS: A NEW PRECONDITIONER BASED ON THE ANALYTIC PARABOLIC FACTORIZATION
• Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
• Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
• The Multifrontal Solution of Indefinite Sparse Symmetric Linear
• A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions
• Nested Dissection of a Regular Finite Element Mesh

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