Substructuring preconditioners for h − p Mortar FEM∗
1 IMATI “E. Magenes”, CNR, via Ferrata 1, 27100 Pavia, Italy.
2 Université de Strasbourg, CNRS, IRMA, UMR 7501, 67000 Strasbourg, France.
3 Laboratoire Jean Kuntzmann, Université Joseph Fourier, UMR 5224, 38041 Grenoble, France.
Accepted: 10 September 2015
We build and analyze a substructuring preconditioner for the Mortar method, applied to elliptic problems, in the h-p finite element framework. Particular attention is given to the construction of the coarse component of the preconditioner in this framework, in which continuity at the cross points is not required. Two variants are proposed: the first one is an improved version of a coarse preconditioner already presented in [S. Bertoluzza and M. Pennacchio, Appl. Numer. Anal. Comput. Math. 1 (2004) 434–454]. The second is new and is built by using a Discontinuous Galerkin interior penalty method as coarse problem. A bound of the condition number is proven for both variants and their efficiency and scalability is illustrated by numerical experiments.
Mathematics Subject Classification: 65N30 / 65N55 / 65F10
Key words: Domain decomposition methods / iterative substructuring / mortar method / h-pFEM
The authors would like to thank Vincent Chabannes for many fruitful discussions. Abdoulaye Samake and Christophe Prud’homme acknowledge the financial support of the project ANR HAMM ANR-2010-COSI-009 and Christophe Prud’homme acknowledges also the support of the LABEX IRMIA. Silvia Bertoluzza acknowledges the financial support of the CNR Short Term Mobility Program 2013 as well as the Center for Modeling and Simulation in Strasbourg (Cemosis). This work was granted access to curie from TGCC@CEA made available by GENCI as well as the IT department (High Performance Computing Pole) of the University of Strasbourg for supporting this work by providing scientific support and access to computing resources. Part of the computing resources were funded by the Equipex Equip@Meso project (Investments for future).
© EDP Sciences, SMAI 2016