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BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields

Journal Article · · Mathematics of Computation
DOI:https://doi.org/10.1090/mcom/3254· OSTI ID:1246885
 [1];  [2];  [3];  [4]
  1. Rutgers Univ., Piscataway, NJ (United States)
  2. Courant Institute of Mathematical Sciences, New York, NY (United States)
  3. King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)
  4. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
+ Show Author Affiliations
Here, a BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a new type of weighted average an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced. Assuming that the subdomains are all built from elements of a coarse triangulation of the given domain, and that in each subdomain the material parameters are consistent, one obtains a bound for the preconditioned linear system's condition number which is independent of the values and jumps of these parameters across the subdomains' interface. Numerical experiments, using the PETSc library, are also presented which support the theory and show the algorithms' effectiveness even for problems not covered by the theory. Also included are experiments with Brezzi-Douglas-Marini finite-element approximations.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1246885
Report Number(s):
SAND2016-0095J; PII: S002557182017032543
Journal Information:
Mathematics of Computation, Journal Name: Mathematics of Computation Vol. 87; ISSN 0025-5718
Country of Publication:
United States
Language:
English

Cited By (3)

Adaptive ACMS: A robust localized Approximated Component Mode Synthesis Method preprint January 2017
Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations: Adaptive BDDC algorithms for plane wave discretization journal August 2018
Parallel adaptive FETI‐DP using lightweight asynchronous dynamic load balancing
  • Klawonn, Axel; Kühn, Martin J.; Rheinbach, Oliver
  • International Journal for Numerical Methods in Engineering, Vol. 121, Issue 4 https://doi.org/10.1002/nme.6237
journal October 2019

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97 MATHEMATICS AND COMPUTING