NUMERICAL-SOLUTION OF EIGENVALUE PROBLEM OF LAPLACE OPERATOR BY A CAPACITANCE MATRIX-METHOD

The problem of finding several eigenfunctions and eigenvalues of the interior Dirichlet problem for Laplace's equation on arbitrary bounded plane regions is considered. Two fast algorithms are combined: an iterative Block Lanczos method and a capacitance matrix method. The capacitance matrix is generated and factored only once for a given problem. In each iteration of the Block Lanczos method, a discrete Helmholtz equation is solved twice on a rectangle at a cost of the order of n2 log2n operations where n is the number of mesh points across the rectangle in which the region is imbedded. © 1978 Springer-Verlag.