Reference : A robust preconditioning technique for the extended finite element method
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
http://hdl.handle.net/10993/15840
A robust preconditioning technique for the extended finite element method
English
[fr] Un préconditionneur robuste pour les éléments finis enrichis
Menk, A. [Robert Bosch GmbH, P. O. Box 300240, 70442 Stuttgart, Germany, Department of Civil Engineering, Glasgow University, Glasgow G12 8LT, United Kingdom]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
2011
International Journal for Numerical Methods in Engineering
85
13
1609-1632
Yes (verified by ORBilu)
International
00295981
[en] Condition number ; Cracks ; Domain decomposition ; Iterative solvers ; Material interfaces ; Preconditioner ; X-FEM ; Condition numbers ; Domain decompositions ; Preconditioners ; Domain decomposition methods ; Number theory ; Numerical methods ; Stiffness ; Stiffness matrix ; Finite element method
[en] 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. © 2010 John Wiley & Sons, Ltd.
Bosch GmbH
Researchers ; Professionals ; Students ; Others
http://hdl.handle.net/10993/15840
10.1002/nme.3032

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2011_Menk_PhD.pdfAlexander Menk's PhD thesisAuthor preprint16.9 MBView/Open

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sol_xvid_001.aviMovie of the fracture of solder joints under thermomechanical fatigue using XFEM3.01 MBView/Open
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sol_mpeg4.aviMovie of the fracture of solder joints under thermomechanical fatigue using XFEM (2)3.5 MBView/Open
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Crack.aviMovie of the fracture of solder joints under thermomechanical fatigue using XFEM (Long)17.09 MBView/Open

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