Wiley InterScience Backfile Collection 1832-2000
Laplace's equation in two dimensions can be solved by a boundary integral method which imposes the required consistency relation between the boundary function and its outward normal gradient. Rather than incorporating this into a standard boundary element approach for the Dirichlet problem, the known boundary function and the unknown boundary gradient are here expressed as truncated Fourier series expansions. The consistency relation then becomes an algebraic relation between expansion coefficients, whose matrix entries can be found by appropriate applications of the fast Fourier transform. This is solved for the boundary gradient coefficients; the solution can then be evaluated at any interior point. Numerical experiments explore the effect of the truncation level, and indicate that reasonable accuracy can be attained without needing a prohibitively large number of Fourier coefficients.
Type of Medium: