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

Journal Article · · Communications on Pure and Applied Mathematics
DOI:https://doi.org/10.1002/cpa.21574· OSTI ID:1141113
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Courant Inst., New York, NY (United States)

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.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1141113
Report Number(s):
SAND2014-2170J; 505383
Journal Information:
Communications on Pure and Applied Mathematics, Vol. 69, Issue 4; Related Information: Proposed for publication in Communications in Pure and Applied Mathematics.; ISSN 0010-3640
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 32 works
Citation information provided by
Web of Science

References (20)

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Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients journal January 2002
Parallel Auxiliary Space AMG for H(Curl) Problems journal June 2009
A Balancing Domain Decomposition by Constraints Deluxe Method for Reissner--Mindlin Plates with Falk--Tu Elements journal January 2015
FETI-DP, BDDC, and block Cholesky methods journal January 2006
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Overlapping Schwarz methods for Maxwell's equations in three dimensions journal October 2000
Dual-primal FETI algorithms for edge finite-element approximations in 3D journal January 2006
An Iterative Substructuring Method for Raviart--Thomas Vector Fields in Three Dimensions journal January 2000

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