Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods

Christoph Hofer

Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods

Numerical Analysis 2016-12-01 v1

Authors: Christoph Hofer

Abstract

In this paper, we present the analysis of the discontinuous Galerkin dual-primal isogeometric tearing and interconnecting method (dG-IETI-DP) for the two-dimensional case where we only consider vertex primal variables. The dG-IETI-DP method is a combination of the dual-primal isogeometric tearing and interconnecting method (IETI-DP) with the discontinuous Galerkin (dG) method. We use the dG method only on the interfaces to couple different patches. This enables us to handle non-matching grids on patch interfaces as well as segmentation crimes (gaps and overlaps) between the patches. The purpose of this paper is to derive quasi-optimal bounds for the condition number of the preconditioned system with respect to the maximal ratio $H/h:=\max_k(H_k/h_k)$ of subdomain diameter and meshsize. We show that the constant is independent of $h_k$ and $H_k$ , but depends on the ratio of meshsizes of neighbouring patches $h_\ell/h_k$ .

Keywords

discontinuous Galerkin dual-primal isogeometric analysis tearing and interconnecting condition number non-matching grids segmentation crimes

Cite

@article{arxiv.1611.10044,
  title  = {Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods},
  author = {Christoph Hofer},
  journal= {arXiv preprint arXiv:1611.10044},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1601.01808

Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods

Abstract

Keywords

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