A BDDC Algorithm with Deluxe Scaling for ThreeDimensional H (curl) Problems
In our paper, we present and analyze a BDDC algorithm for a class of elliptic problems in the threedimensional 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.
 Authors:

^{[1]};
^{[2]}
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Courant Inst., New York, NY (United States)
 Publication Date:
 Report Number(s):
 SAND20142170J
Journal ID: ISSN 00103640; 505383
 Grant/Contract Number:
 AC0494AL85000
 Type:
 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 00103640
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1141113
Dohrmann, Clark R., and Widlund, Olof B.. A BDDC Algorithm with Deluxe Scaling for ThreeDimensional H (curl) Problems. United States: N. p.,
Web. doi:10.1002/cpa.21574.
Dohrmann, Clark R., & Widlund, Olof B.. A BDDC Algorithm with Deluxe Scaling for ThreeDimensional H (curl) Problems. United States. doi:10.1002/cpa.21574.
Dohrmann, Clark R., and Widlund, Olof B.. 2015.
"A BDDC Algorithm with Deluxe Scaling for ThreeDimensional H (curl) Problems". United States.
doi:10.1002/cpa.21574. https://www.osti.gov/servlets/purl/1141113.
@article{osti_1141113,
title = {A BDDC Algorithm with Deluxe Scaling for ThreeDimensional H (curl) Problems},
author = {Dohrmann, Clark R. and Widlund, Olof B.},
abstractNote = {In our paper, we present and analyze a BDDC algorithm for a class of elliptic problems in the threedimensional 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.},
doi = {10.1002/cpa.21574},
journal = {Communications on Pure and Applied Mathematics},
number = 4,
volume = 69,
place = {United States},
year = {2015},
month = {4}
}