VECTORIZED STRONGLY IMPLICIT SOLVING PROCEDURE FOR A SEVEN-DIAGONAL COEFFICIENT MATRIX

The paper presents an extension of Stone's(1) 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.