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A scalable approximate inverse block preconditioner for an incompressible magnetohydrodynamics model problem. (English) Zbl 1428.76177

Summary: We introduce a new approximate inverse preconditioner for a mixed finite element discretization of an incompressible magnetohydrodynamics model problem. The derivation exploits the nullity of the discrete curl-curl operator in the Maxwell subproblem. We show that the inverse of the coefficient matrix contains zero blocks and use discretization considerations to obtain a practical preconditioner based on further sparsification. We demonstrate the viability of our approach with a set of numerical experiments.

MSC:

76M99 Basic methods in fluid mechanics
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F50 Computational methods for sparse matrices
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics

Software:

PETSc; FEniCS; hypre
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Full Text: DOI

References:

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