Construction of some iterative methods for solving boundary element linear systems (Q1347143)

The boundary element method is now being used to solve a wide class of boundary value problems. In order for this method to be competitive with existing methods for large scale problems, economical methods for solving algebraic boundary element linear systems are sought. Some general types of iterative methods for solving such algebraic equations are discussed. In the most popular collocation version of the boundary element method the algebraic system of linear equations has a full coefficient matrix with no special structure. For such linear systems some successive overrelaxation (SOR-type) and preconditioned conjugate gradient (PCG-type) iterative methods are proposed and compared. The effect of the locations of the known components of the solutions vector on the rate of convergence is also investigated. Results obtained in the paper demonstrate that the PCG-type methods can be superior to the SOR-type methods with respect to the rate of convergence.