ITERATIVE SOLUTION OF SYSTEMS OF EQUATIONS IN THE DUAL RECIPROCITY BOUNDARY-ELEMENT METHOD FOR THE DIFFUSION EQUATION

In this paper the diffusion equation is solved in two-dimensional geom etry by the dual reciprocity boundary element method (DRBEM). It is st ructured by fully implicit discretization over time and by weighting w ith the fundamental solution of the Laplace equation. The resulting do main integral of the diffusive term is transformed into two boundary i ntegrals by using Green's second identity, and the domain integral of the transience term is converted into a finite series of boundary inte grals by using dual reciprocity interpolation based on scaled augmente d thin plate spline global approximation functions. Straight line geom etry and constant field shape functions for boundary discretization ar e employed. The described procedure results in systems of equations wi th fully populated unsymmetric matrices. In the case of solving large problems, the solution of these systems by direct methods may be very time consuming. The present study investigates the possibility of usin g iterative methods for solving these systems of equations. It was dem onstrated that Krylov-type methods like CGS and GMRES with simple Jaco bi preconditioning appeared to be efficient and robust with respect to the problem size and time step magnitude. This paper can be considere d as a logical starting point for research of iterative solutions to D RBEM systems of equations. (C) 1998 John Wiley & Sons, Ltd.