On fast direct methods for solving elliptic equations over nonrectangular regions
In this paper, two methods based on the symmetric marching technique (SMT) are presented for the solution of elliptic equations over nonrectangular regions. Method I illustrates the direct adaptation of the SMT to irregular geometries. In method II, an efficient implementation of the capacitance matrix method has been considered using SMT. The favorable characteristics of the SMT for solving the Poisson equation with several right hand side functions and different boundary conditions without extra computational effort have been exploited for the last generation of the capacitance matrix. The successful application of the SMT combined with quasilinearization to solve mildly nonlinear elliptic equations is also described. Several test examples have been solved to demonstrate the efficiency of the proposed methods.