Sparse approximation for solving integral equations with oscillatory kernels. (English) Zbl 0749.65093

Canning, Francis X.

SIAM J. Sci. Stat. Comput. 13, No. 1, 71-87 (1992).

An integral equation formulation of Helmholtz’s equation is considered as an example of a problem with an oscillatory kernel. A class of transformations of the usual matrix formulations of integral equations is presented in order to generate a sparse \(N\times N\) matrix from a full \(N\times N\) matrix. The method reduces the storage and the operations per iteration from \(N^ 2\) to \(O(N)\).

Reviewer: T.Tang (Burnaby)

MSC:

65R20	Numerical methods for integral equations
65N38	Boundary element methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
65F35	Numerical computation of matrix norms, conditioning, scaling
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

integral equations; sparse matrices; iterative methods; preconditioner; Helmholtz equation; oscillatory kernel