On fast direct methods for solving elliptic equations over nonrectangular regions (Q1102723)

Two method are presented for numerically solving the Poisson equation on nonrectangular regions. Both are based on a symmetric marching technique (SMT) developed by the authors and \textit{R. Sanker} [ibid. 12, 187-198 (1983; Zbl 0513.65065)]. The first method applies directly and modifies an idea developed by \textit{P. J. Roache} [Lect. Notes Phys. 8, 48-53 (1971; Zbl 0236.76019)]. The second method combines SMT with the capacitance matrix method as developed by \textit{R. W. Hockney} [POT4 - A fast direct Poisson solver for the rectangle allowing some mixed boundary conditions and internal electrodes - IBM Research, R. C. 2870 (1970)]. An extension of the methods to some mildly nonlinear elliptic equations is included. The two final sections in the paper exhibit resuts from several tests and a discussion of how the methods work, when compared with Roache's method.