A Time-Parallel Multigrid Method for Two-Phase Stefan Problems

Ronald H. W. Hoppe and \underline{Frank Wagner}

Lehrstuhl für Angewandte Mathematik I, Universität Augsburg Universitätsstr.14, D-86159 Augsburg e-Mail: Frank.Wagner@Math.Uni-Augsburg.DE

April 17, 1996

Abstract

We present time-parallel multigrid methods for the efficient numerical solution of moving boundary problems of two-phase Stefan type describing heat transfer processes with a change of phase. Using either a direct approach to the nonlinear enthalpy formulation of the problem or a linearization thereof based on semigroup theory, parallelism comes in by the simultaneous application of multigrid methods to a sequence of backward Euler steps in time. Numerical results obtained by the implementation of the algorithm on the IBM SP2 using the MPI Message-Passing Interface Standard are given in terms of various efficiency rates.