An iterative solver for the 3D Helmholtz equation

DOI10.1016/j.jcp.2017.05.026zbMath1378.35088OpenAlexW2615942622MaRDI QIDQ1692026

Dmitry Neklyudov, Mikhail Belonosov, Victor Kostin, Vladimir Tcheverda, Maxim N. Dmitriev

Publication date: 26 January 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2017.05.026

zbMATH Keywords

modelingpreconditioningiterative methodsHelmholtz equationacoustics

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for partial differential equations, boundary value problems (65N99) Methods of ordinary differential equations applied to PDEs (35A24)

Related Items (4)

Unnamed Item ⋮ A new eighth-order implicit finite difference method to solve the three-dimensional Helmholtz equation ⋮ Modeling the long-range wave propagation by a split-step wavelet method ⋮ Contraction operator transformation for the complex heterogeneous Helmholtz equation

Uses Software

• BLAS
• MKL
• Algorithm 913

Cites Work

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• A perfectly matched layer for the Helmholtz equation in a semi-infinite strip
• Accelerating the shifted Laplace preconditioner for the Helmholtz equation by multilevel deflation
• On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian
• Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics
• Fast Fourier transform: algorithms and applications
• Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
• Basic linear algebra subprograms (BLAS) on the CDC CYBER 205
• On a class of preconditioners for solving the Helmholtz equation
• Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems
• Algorithm 913
• Shifted-Laplacian Preconditioners for Heterogeneous Helmholtz Problems
• IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Reflectionless Sponge Layers as Absorbing Boundary Conditions for the Numerical Solution of Maxwell Equations in Rectangular, Cylindrical, and Spherical Coordinates

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