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A new block parallel SOR method and its analysis. (English) Zbl 1100.65032
The author introduces a new mesh domain partitioning and ordering and proposes a new block parallel successive overrelaxation (BPSOR) method for numerically solving 2-dimensional (2D) or three dimensional (3D) elliptic boundary problems. A general mathematical analysis shows that the BPSOR method can have the same asymptotic convergence rate as the corresponding sequential block SOR method if the coefficient matrix of the block linear system is “consistently ordered”.

65F10 Iterative numerical methods for linear systems
65Y05 Parallel numerical computation
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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