We propose a family of preconditioners for linear systems of equations arising from a piecewise polynomial symmetric interior penalty discontinuous Galerkin discretization of H(curl,ω)-elliptic boundary value problems on conforming meshes. The design and analysis of the proposed preconditioners rely on the auxiliary space method (ASM) employing an auxiliary space of H(curl,ω)-conforming finite element functions together with a relaxation technique (local smoothing). On simplicial meshes, the proposed preconditioner enjoys asymptotic optimality with respect to mesh refinement. It is also robust with respect to jumps in the coefficients ? and b in the second-and zeroth-order parts of the operator, respectively, except when the problem changes from curl-dominated to reaction-dominated and vice versa. On quadrilateral/hexahedral meshes some of the proposed ASM solvers may fail, since the related H(curl,ω)-conforming finite element space does not provide a spectrally accurate discretization. Extensive numerical experiments are included to verify the theory and assess the performance of the preconditioners.

Ayuso De Dios, B., Hiptmair, R., Pagliantini, C. (2017). Auxiliary space preconditioners for SIP-DG discretizations of H(curl)-elliptic problems with discontinuous coefficients. IMA JOURNAL OF NUMERICAL ANALYSIS, 37(2), 646-686 [10.1093/imanum/drw018].

Auxiliary space preconditioners for SIP-DG discretizations of H(curl)-elliptic problems with discontinuous coefficients

Ayuso De Dios, B;
2017

Abstract

We propose a family of preconditioners for linear systems of equations arising from a piecewise polynomial symmetric interior penalty discontinuous Galerkin discretization of H(curl,ω)-elliptic boundary value problems on conforming meshes. The design and analysis of the proposed preconditioners rely on the auxiliary space method (ASM) employing an auxiliary space of H(curl,ω)-conforming finite element functions together with a relaxation technique (local smoothing). On simplicial meshes, the proposed preconditioner enjoys asymptotic optimality with respect to mesh refinement. It is also robust with respect to jumps in the coefficients ? and b in the second-and zeroth-order parts of the operator, respectively, except when the problem changes from curl-dominated to reaction-dominated and vice versa. On quadrilateral/hexahedral meshes some of the proposed ASM solvers may fail, since the related H(curl,ω)-conforming finite element space does not provide a spectrally accurate discretization. Extensive numerical experiments are included to verify the theory and assess the performance of the preconditioners.
Articolo in rivista - Articolo scientifico
discontinuous Galerkin methods; H(curl; Ω)-elliptic problems; auxiliary space preconditioning; discontinuous coefficients
English
2017
37
2
646
686
partially_open
Ayuso De Dios, B., Hiptmair, R., Pagliantini, C. (2017). Auxiliary space preconditioners for SIP-DG discretizations of H(curl)-elliptic problems with discontinuous coefficients. IMA JOURNAL OF NUMERICAL ANALYSIS, 37(2), 646-686 [10.1093/imanum/drw018].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/218112
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