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Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning

Författare

Summary, in English

We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, mixed, and tested on some familiar problems in materials science. The recursive compressed inverse preconditioning, the major novelty of the paper, turns out to be particularly powerful and, when it applies, eliminates the need for mesh grading completely. In an electrostatic example for a multiphase granular material with about two thousand corners and triple junctions and a conductivity ratio between phases up to a million we compute a common functional of the solution with an estimated relative error of 10-12. In another example, five times as large but with a conductivity ratio of only a hundred, we achieve an estimated relative error of 10-14.

Avdelning/ar

Publiceringsår

2008

Språk

Engelska

Sidor

8820-8840

Publikation/Tidskrift/Serie

Journal of Computational Physics

Volym

227

Issue

20

Dokumenttyp

Artikel i tidskrift

Förlag

Elsevier

Ämne

  • Mathematics

Nyckelord

  • Corner singularity Multiphase material Triple-junction Integral equation Mesh grading Conductivity

Status

Published

Forskningsgrupp

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications

ISBN/ISSN/Övrigt

  • ISSN: 0021-9991