AN OPERATOR SPLITTING PRECONDITIONER FOR MATRICES ARISING FROM A WAVELET BOUNDARY ELEMENT METHOD FOR THE HELMHOLTZ EQUATION

DOI10.1142/S0219691305001044zbMath1084.65044MaRDI QIDQ5716164

Paul J. Harris, Ke Chen, Stuart Hawkins

Publication date: 9 January 2006

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

zbMATH Keywords

Galerkin methodnumerical resultsscatteringpreconditioningwaveletHelmholtz equationboundary element

Mathematics Subject Classification ID

Numerical methods for wavelets (65T60) 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)

Cites Work

• Biorthogonal spline wavelets on the interval -- stability and moment conditions
• On efficient preconditioners for iterative solution of a Galerkin boundary element equation for the three-dimensional exterior Helmholtz problem
• Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Orthonormal bases of compactly supported wavelets
• Biorthogonal bases of compactly supported wavelets
• Boundary integral solutions of three dimensional acoustic radiation problems
• On a Class of Preconditioning Methods for Dense Linear Systems from Boundary Elements
• Composite wavelet bases for operator equations
• An Improved Discrete Wavelet Transform Preconditioner for Dense Matrix Problems
• Wavelet Galerkin Algorithms for Boundary Integral Equations
• Wavelet Methods for Second-Order Elliptic Problems, Preconditioning, and Adaptivity
• The application of integral equation methods to the numerical solution of some exterior boundary-value problems
• Methods of conjugate gradients for solving linear systems
• Efficient preconditioners for iterative solution of the boundary element equations for the three-dimensional Helmholtz equation

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