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A robust preconditioning technique for the extended finite element method

Menk, Alexander and Bordas, Stéphane Pierre Alain ORCID: 2011. A robust preconditioning technique for the extended finite element method. International Journal for Numerical Methods in Engineering 85 (13) , pp. 1609-1632. 10.1002/nme.3032

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The extended finite element method enhances the approximation properties of the finite element space by using additional enrichment functions. But the resulting stiffness matrices can become ill-conditioned. In that case iterative solvers need a large number of iterations to obtain an acceptable solution. In this paper a procedure is described to obtain stiffness matrices whose condition number is close to the one of the finite element matrices without any enrichments. A domain decomposition is employed and the algorithm is very well suited for parallel computations. The method was tested in numerical experiments to show its effectiveness. The experiments have been conducted for structures containing cracks and material interfaces. We show that the corresponding enrichments can result in arbitrarily ill-conditioned matrices. The method proposed here, however, provides well-conditioned matrices and can be applied to any sort of enrichment. The complexity of this approach and its relation to the domain decomposition is discussed. Computation times have been measured for a structure containing multiple cracks. For this structure the computation times could be decreased by a factor of 2.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: X-FEM; condition number; preconditioner; iterative solvers; cracks; material interfaces; domain decomposition
Publisher: Wiley
ISSN: 0029-5981
Last Modified: 18 Oct 2022 13:49

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