Geodesic
Substructuring preconditioners for h-p Mortar FEM
Bertoluzza, Silvia1  ; Pennacchio, Micol1 ; Prud’homme, Christophe2  ; Samake, Abdoulaye3 
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1057-1082

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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.

DOI : 10.1051/m2an/2015065
Classification : 65N30, 65N55, 65F10
Keywords: Domain decomposition methods, iterative substructuring, mortar method, h-pFEM

Bertoluzza, Silvia 1 ; Pennacchio, Micol 1 ; Prud’homme, Christophe 2 ; Samake, Abdoulaye 3

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. 
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     title = {Substructuring preconditioners for $h - p$ {Mortar} {FEM}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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Bertoluzza, Silvia; Pennacchio, Micol; Prud’homme, Christophe; Samake, Abdoulaye. Substructuring preconditioners for $h - p$ Mortar FEM. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1057-1082. doi: 10.1051/m2an/2015065

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