A major computational effort in the Finite Element (FE) integration of a coupled consolidation model is the repeated solution in time of the resulting discretized indefinite equations. Because of ill-conditioning, the iterative solution may require the assessment of a suitable preconditioner to guarantee convergence. At each time step, the solution of the linear system Ax = b, where A is a 2x2 block saddle-point matrix, is performed by a Krylov subspace method preconditioned by M−1 preserving the same block structure as A. An efficient way to apply the preconditioner to a vector is developed. Numerical results onto test problems of large size reveal that the proposed preconditioner can be more efficient than the standard ILU/ILUT preconditioners.
Efficient preconditioners for Krylov subspace methods in the solution of coupled consolidation problems
BERGAMASCHI, LUCA;FERRONATO, MASSIMILIANO;GAMBOLATI, GIUSEPPE
2006
Abstract
A major computational effort in the Finite Element (FE) integration of a coupled consolidation model is the repeated solution in time of the resulting discretized indefinite equations. Because of ill-conditioning, the iterative solution may require the assessment of a suitable preconditioner to guarantee convergence. At each time step, the solution of the linear system Ax = b, where A is a 2x2 block saddle-point matrix, is performed by a Krylov subspace method preconditioned by M−1 preserving the same block structure as A. An efficient way to apply the preconditioner to a vector is developed. Numerical results onto test problems of large size reveal that the proposed preconditioner can be more efficient than the standard ILU/ILUT preconditioners.
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