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Auxiliary Space Preconditioner for a Discontinuous Galerkin Discretization of H(curl)-Elliptic Problems on Hexahedral Meshes

by B. Ayuso deDios and R. Hiptmair and C. Pagliantini

(Report number 2017-26)

Abstract
We present a family of preconditioners based on the auxiliary space method for a discontinuous Galerkin discretization on cubical meshes of \(H(\mathbf{curl};\Omega)\)-elliptic problems with possibly discontinuous coefficients. We address the influence of possible discontinuities in the coefficients on the asymptotic performance of the proposed solvers and present numerical results in two dimensions.

Keywords: Auxiliary space preconditioning, discrete differential forms, discontinuous Galerkin method

@Techreport{AHP17_722,
  author = {B. Ayuso deDios and R. Hiptmair and C. Pagliantini},
  title = {Auxiliary Space Preconditioner for a Discontinuous Galerkin Discretization of H(curl)-Elliptic Problems on Hexahedral Meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-26},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-26.pdf },
  year = {2017}
}

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