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.
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