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An aggregation-based domain decomposition preconditioner for groundwater flow. (English) Zbl 1036.65109

The authors analyze the theoretical and computational aspects of the aggregation-based domain decomposition preconditioner applied to a Bi-CGSTAB iterative solver. The solver is used to integrate numerically Laplace’s equation and Richards’ (nonlinear) equation. The numerical experiments exhibit excellent scalability.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
86A05 Hydrology, hydrography, oceanography
65H10 Numerical computation of solutions to systems of equations
65F35 Numerical computation of matrix norms, conditioning, scaling
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35Q35 PDEs in connection with fluid mechanics

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