Vectorized strongly implicit solving procedure for a seven‐diagonal coefficient matrix

Abstract

The paper presents an extension of Stone’s1 strongly implicit procedure for solving linear equation systems resulting from the discretization of partial differential equations to three‐dimensional problems. The solver is applicable to seven‐diagonal coefficient matrices, as are obtained when central‐difference approximations are used for discretization. The algorithm is implemented in a way which allows vector processing on modern supercomputers, in spite of its recursive structure. Other solvers, using incomplete lower‐upper decomposition (ILU), can be vectorized in the same way. Test calculations show solver performance of about 150 Mflops on CRAY—YMP and over 200 Mflops on FUJITSU—VP200 computers. A listing of the FORTRAN code is provided.