Fourier Series Solutions to Poisson's Equation in Rectangularly Decomposable Regions
Timothy N. Philips · IMA Journal of Numerical Analysis · 1989
Fourier senes solutions to Poisson problems defined in rectangularly decomposable regions are found by matching solutions in a weak sense across the interfaces dividing subregions. The matching process produces an infinite system of algebraic equations for the unknown expansion coefficients. Complex analysis is used to investigate theoretically the conditioning of the coefficient matrix for both the C0 and C1 matching problems. The former is shown to be not well-defined whereas the latter is extremely well-conditioned. Furthermore, the analysis of the coefficient matrix for the weak C1 problem suggests a rapidly convergent iterative method for solving the truncated algebraic system for the expansion coefficients. Accurate approximations are obtained after a handful of iterations and with few degrees of freedom.