A multigrid-based preconditioned solver for the Helmholtz equation with a discretization by 25-point difference scheme

DOI10.1016/j.matcom.2015.01.009OpenAlexW632219454MaRDI QIDQ2228668

Tingting Wu, Dongsheng Cheng, Zhi-yong Liu

Publication date: 19 February 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2015.01.009

zbMATH Keywords

Helmholtz equationmultigridpreconditionerprolongation operator

Mathematics Subject Classification ID

Dynamical systems and ergodic theory (37-XX) Numerical analysis (65-XX)

Related Items (5)

Nine-point compact sixth-order approximation for two-dimensional nonlinear elliptic partial differential equations: application to bi- and tri-harmonic boundary value problems ⋮ A new finite difference scheme for the 3D Helmholtz equation with a preconditioned iterative solver ⋮ An optimal compact sixth-order finite difference scheme for the Helmholtz equation ⋮ A robust optimal finite difference scheme for the three-dimensional Helmholtz equation ⋮ A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes

Cites Work

• Unnamed Item
• Application of the shifted-Laplace preconditioner for iterative solution of a higher order finite element discretisation of the vector wave equation: first experiences
• GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method
• An optimal 25-point finite difference scheme for the Helmholtz equation with PML
• A perfectly matched layer for the Helmholtz equation in a semi-infinite strip
• Compact finite difference schemes of sixth order for the Helmholtz equation
• A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
• A perfectly matched layer for the absorption of electromagnetic waves
• High-order finite difference methods for the Helmholtz equation
• A multigrid-based preconditioned Krylov subspace method for the Helmholtz equation with PML
• Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
• A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization
• Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
• Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Absorbing boundary conditions for electromagnetic wave propagation
• An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
• Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics
• A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

This page was built for publication: A multigrid-based preconditioned solver for the Helmholtz equation with a discretization by 25-point difference scheme