Vectorized strongly implicit solving procedure for a seven-diagonal coefficient matrix
H.-J. Leister, Milovan Perić · International Journal of Numerical Methods for Heat & Fluid Flow · 1994
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.