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

In our 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/his 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 our 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. Furthermore, numerical examples are presented to confirm the theory and demonstrate the importance of the new averaging approach in certain cases.
 [1] ;  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Courant Inst., New York, NY (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0010-3640; 505383
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Communications on Pure and Applied Mathematics
Additional Journal Information:
Journal Volume: 69; Journal Issue: 4; Related Information: Proposed for publication in Communications in Pure and Applied Mathematics.; Journal ID: ISSN 0010-3640
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States