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Convergence and optimization of the parallel method of simultaneous directions for the solution of elliptic problems. (English) Zbl 1156.65092

The authors perform a detailed analysis of the convergence and optimization of parallel fractional step methods and simultaneous directions methods for elliptic problems. They describe the behavior of the method and specify the good choice of the parameters. Also, they study the efficiency of the parallelization. The theoretical results are confirmed with some 2D, 3D and higher dimensional test problems.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65Y05 Parallel numerical computation
35J25 Boundary value problems for second-order elliptic equations
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