A FOURIER BOUNDARY INTEGRAL METHOD FOR SOLVING LAPLACES-EQUATION IN 2DIMENSIONS

Laplace's equation in two dimensions can be solved by a boundary integ ral method which imposes the required consistency relation between the boundary function and its outward normal gradient. Rather than incorp orating this into a standard boundary element approach for the Dirichl et problem, the known boundary function and the unknown boundary gradi ent are here expressed as truncated Fourier series expansions. The con sistency relation then becomes an algebraic relation between expansion coefficients, whose matrix entries can be found by appropriate applic ations of the fast Fourier transform. This is solved for the boundary gradient coefficients; the solution can then be evaluated at any inter ior point. Numerical experiments explore the effect of the truncation level, and indicate that reasonable accuracy can be attained without n eeding a prohibitively large number of Fourier coefficients.