A finite element - capacitance method for elliptic problems on regions partitioned into subregions (Q1060547)

A method is described for the solution of linear equations arising in the finite element method with triangular elements and linear approximation for second order elliptic equations in a bounded region with Dirichlet boundary conditions. This method reduces the original problem to several subproblems considered on subregions and an auxiliary problem corresponding to the nodes belonging to the partition curves. The subproblems are solved by direct methods. For the solution of the auxiliary problem the author develops very efficient iterative methods using FFT: the generalized conjugate gradient method in the symmetric case, and the generalized minimum residual method in the nonsymmetric case.