ON THE NUMERICAL-SOLUTION OF PARTIAL-DIFFERENTIAL EQUATIONS WITH 2 SPATIAL SCALES

A numerical solver developed for the solution of parabolic partial dif ferential equations involving two spatial scales is presented. The equ ations are discretized using the finite volume method, and the resulti ng system of ordinary differential equations is solved using the stiff code DASSL. The solver has been implemented in the form of a collecti on of FORTRAN subroutines. The large sparse linear systems which occur during the solution process are solved by a direct efficient method b ased on a complete LU factorization. The method is fully described in the paper. The storage space needed by the algorithm is reduced by a f actor of 3m/4, m being the number of micro grid points, with respect t o the standard LINPACK band solver. A comparison of the number of floa ting point operations involved in the different algorithms shows that this approach reduces the operation count for the factorization phase by a factor of about m, with respect to the LINPACK solver. For the su bstitution phase the improvement ratio is approximately equal to 3m/4. Copyright (C) 1996 Elsevier Science Ltd