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Dual-Primal FETI algorithms for edge element approximations: Three-dimensional h finite elements on shaperegular meshes

by A. Toselli

(Report number 2005-03)

Abstract
A family of dual-primal FETI methods for edge element approximations in three dimensions is proposed and analyzed. The key part of this work relies on the observation that for these finite element spaces there is a strong coupling between degrees of freedom associated to subdomain edges and faces and a local change of basis is therefore necessary. The primal constraints are associated with subdomain edges. We propose three methods. They ensure a condition number that is independent of the number of substructures and possibly large jumps of one of the coefficients of the original problem, and only depends on the number of unknowns associated with a single substructure, as for the corresponding methods for continuous nodal elements. A polylogarithmic dependence is shown for two algorithms. Numerical results validating our theoretical bounds are given.

Keywords: Edge elements, Maxwell's equations, finite elements, domain decomposition, FETI, preconditioners, heterogeneous coefficients

@Techreport{T05_342,
  author = {A. Toselli},
  title = {Dual-Primal FETI algorithms for edge element approximations: Three-dimensional h finite elements on shaperegular meshes},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2005-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2005/2005-03.pdf },
  year = {2005}
}

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