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Successive peripheral over-relaxation and other block methods

1976; Elsevier BV; Volume: 21; Issue: 1 Linguagem: Inglês

10.1016/0021-9991(76)90017-6

1090-2716

Austin R. Benson, David J. Evans,

Pain Management and Treatment

Successive 1-line and 2-line over-relaxation techniques for solving self-adjoint second-order elliptic partial-differential equations in a rectangle subject to a periodicity condition in one coordinate direction are shown to be equivalent to successive peripheral techniques in plane regions with holes. Algorithms are given for solving the resulting sets of equations and the numerical results obtained substantiate the equivalence. An intuitive comparison is also made between successive peripheral over-relaxation and the more usual 1-line and 2-line blocks for the model Dirichlet problem. It is concluded that the 1-peripheral block (SPQR) corresponds more to the 2-line method (S2LOR) rather than to the single line grouping (SLOR).