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Preconditioning the coarse problem of BDDC methods – three-level, algebraic multigrid, and vertex-based preconditioners. (English) Zbl 1447.65122
The paper introduces three novel approximate preconditioners for balancing domain decomposition by contsrtains: a preconditioner using algebraic multigrid, a three-level balancing method, and a vertex-based preconditioner using a Gauss-Seidel method. The study goes in deep, the condition number bounds for all three approximate preconditioners being calculated. The numerical tests are focusing on linear elasticity problems. The proposed preconditioners are properly compared in three spatial dimensions with the aim to show their computing time and parallel scalability.

MSC:
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
65Y05 Parallel numerical computation
Software:
BDDC; BDDCML; BoomerAMG; PETSc
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References:
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