A BDDC Algorithm with Deluxe Scaling for Three-Dimensional H(curl) Problems

Clark R. Dohrmann, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

In this paper, we present and analyze a BDDC algorithm for a class of elliptic problems in the three-dimensional H(curl) space. Compared with existing results, our condition number estimate requires fewer assumptions and also involves two fewer powers of log(H/h), making it consistent with optimal estimates for other elliptic problems. Here, H/h is the maximum of Hi/hi over all subdomains, where Hi and hi are the diameter and the smallest element diameter for the subdomain Ωi. The analysis makes use of two recent developments. The first is a new approach to averaging across the subdomain interfaces, while the second is a new technical tool that allows arguments involving trace classes to be avoided. Numerical examples are presented to confirm the theory and demonstrate the importance of the new averaging approach in certain cases.

Original languageEnglish (US)
Pages (from-to)745-770
Number of pages26
JournalCommunications on Pure and Applied Mathematics
Volume69
Issue number4
DOIs
StatePublished - Apr 1 2016

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Curl
Elliptic Problems
Averaging
Scaling
Three-dimensional
Condition number
Estimate
Trace
Numerical Examples
Demonstrate
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A BDDC Algorithm with Deluxe Scaling for Three-Dimensional H(curl) Problems. / Dohrmann, Clark R.; Widlund, Olof B.

In: Communications on Pure and Applied Mathematics, Vol. 69, No. 4, 01.04.2016, p. 745-770.

Research output: Contribution to journalArticle

Dohrmann, Clark R. ; Widlund, Olof B. / A BDDC Algorithm with Deluxe Scaling for Three-Dimensional H(curl) Problems. In: Communications on Pure and Applied Mathematics. 2016 ; Vol. 69, No. 4. pp. 745-770.
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