Numerical Solution of Helmholtz's Equation by the Capacitance Matrix Method.

摘要

The computer solution of the Helmholtz equation is discussed. Problems can be treated on bounded regions which do not allow for separation of variables. The topics treated in the report are as follows:certain results from classical potential theory,the imbedding of discrete Poisson problems, a capacitance matrix method for the Dirichlet case, a capacitance matrix method for the Neumann case,the Fourier--Toeplitz method and the fast generation of the capacitance matrix,the conjugate gradient method,previous work on capacitance matrix methods,numeral experiments,and outline of a computer program for the numerical solution of the interior Helmholtz equation in two variables with the Dirichlet and Neumann boundary conditions by finite difference methods. 3figures, 8tables.