PRECONDITIONERS FOR THE P-VERSION OF THE GALERKIN METHOD FOR A COUPLED FINITE ELEMENT BOUNDARY ELEMENT SYSTEM/

We propose and analyze efficient preconditioners for solving systems o f equations arising from the p-version for the finite element/boundary element coupling. The first preconditioner amounts to a block jacobi method, whereas the second one is partly given by diagonal scaling. We use the generalized minimum residual method for the solution of the l inear system. For our first preconditioner, the number of iterations o f the GMRES necessary to obtain a given accuracy grows like log(2) p, where p is the polynomial degree of the ansatz functions. The second p reconditioner, which is more easily implemented, leads to a number of iterations that behave like p log(3) p. Computational results are pres ented to support this theory. (C) 1998 John Wiley & Sons, Inc.