A BDDC Algorithm with Deluxe Scaling for Three‐Dimensional H(curl) Problems. Issue 4 (28th April 2015)

• Record Type: Journal Article
• Authors: Dohrmann, Clark R.; Widlund, Olof B.
• Is Part Of: Communications on pure and applied mathematics. Volume 69:Issue 4(2016:Apr.)
• Page Start: 745
• Page End: 770
• Publication Date: 2015-04-28
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21574
• Languages: English
• ISSNs: 0010-3640

Abstract

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 H i / h i over all subdomains, where H i and h i are the diameter and the smallest element diameter for the subdomain Ω i . 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. © 2016 Wiley Periodicals, Inc.