Incomplete block factorization preconditioning for linear systems arising in the numerical solution of the Helmholtz equation

DOI10.1016/0168-9274(95)00094-1zbMath0854.65086OpenAlexW2123391355MaRDI QIDQ1917436

Chun-Hua Guo

Publication date: 6 January 1997

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00094-1

zbMATH Keywords

convergencenumerical example\(M\)-matrixHelmholtz equationfinite differenceDirichlet boundary value problembiconjugate gradient methodblock-tridiagonal matrixconjugate gradient type methodsincomplete block factorizationscomplex system matrixeffective preconditioner

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (11)

Unnamed Item ⋮ A splitting method for complex symmetric indefinite linear system ⋮ Modified complex-symmetric and skew-Hermitian splitting iteration method for a class of complex-symmetric indefinite linear systems ⋮ Several variants of the Hermitian and skew-Hermitian splitting method for a class of complex symmetric linear systems ⋮ A splitting iterative method for the discrete dynamic linear systems ⋮ A modified SSOR preconditioning strategy for Helmholtz equations ⋮ Positive stable preconditioners for symmetric indefinite linear systems arising from Helmholtz equations ⋮ A preconditioner based on a splitting-type iteration method for solving complex symmetric indefinite linear systems ⋮ A PRECONDITIONED METHOD FOR THE SOLUTION OF THE ROBBINS PROBLEM FOR THE HELMHOLTZ EQUATION ⋮ On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors ⋮ A new two-parameter iteration method for indefinite complex symmetric linear systems

Cites Work

• An iterative method for the Helmholtz equation
• Some results on sparse block factorization iterative methods
• Modified block-approximate factorization strategies
• On approximate factorization methods for block matrices suitable for vector and parallel processors
• A general incomplete block-matrix factorization method
• Preconditioning indefinite discretization matrices
• Block Preconditioning for the Conjugate Gradient Method
• NOTE ON M-MATRICES
• On Sparse Block Factorization Iterative Methods
• Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Indefinite elliptic problem preconditioning
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• A Generalization of the Conjugate-Gradient Method to Solve Complex Systems
• Unnamed Item

This page was built for publication: Incomplete block factorization preconditioning for linear systems arising in the numerical solution of the Helmholtz equation