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

Oh, Duk -Soon; Widlund, Olof B.; Zampini, Stefano; Dohrmann, Clark R.

doi:10.1090/mcom/3254

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

Abstract

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.

Authors:

Oh, Duk -Soon ^[1]; Widlund, Olof B. ^[2]; Zampini, Stefano ^[3]; Dohrmann, Clark R. ^[4]

Rutgers Univ., Piscataway, NJ (United States)
Courant Institute of Mathematical Sciences, New York, NY (United States)
King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Wed Jun 21 00:00:00 EDT 2017

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1246885

Report Number(s):: SAND2016-0095J
Journal ID: ISSN 0025-5718; PII: S002557182017032543

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Mathematics of Computation

Additional Journal Information:: Journal Volume: 87; Journal ID: ISSN 0025-5718

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Oh, Duk -Soon, Widlund, Olof B., Zampini, Stefano, and Dohrmann, Clark R. BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields.  United States: N. p., 2017. 
Web.  doi:10.1090/mcom/3254.

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                    Oh, Duk -Soon, Widlund, Olof B., Zampini, Stefano, & Dohrmann, Clark R. BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields.  United States.  https://doi.org/10.1090/mcom/3254

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                    Oh, Duk -Soon, Widlund, Olof B., Zampini, Stefano, and Dohrmann, Clark R. Wed .  
"BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields".  United States.  https://doi.org/10.1090/mcom/3254.  https://www.osti.gov/servlets/purl/1246885.

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@article{osti_1246885,

  title        = {BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields},

  author       = {Oh, Duk -Soon and Widlund, Olof B. and Zampini, Stefano and Dohrmann, Clark R.},

  abstractNote = {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.},

  doi          = {10.1090/mcom/3254},

  journal      = {Mathematics of Computation},

  number       = ,

  volume       = 87,

  place        = {United States},

  year         = {Wed Jun 21 00:00:00 EDT 2017},

  month        = {Wed Jun 21 00:00:00 EDT 2017}

}

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Works referencing / citing this record:

Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations: Adaptive BDDC algorithms for plane wave discretization
journal, August 2018

Peng, Jie; Wang, Junxian; Shu, Shi
International Journal for Numerical Methods in Engineering, Vol. 116, Issue 10-11
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Parallel adaptive FETI‐DP using lightweight asynchronous dynamic load balancing
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International Journal for Numerical Methods in Engineering, Vol. 121, Issue 4
DOI: 10.1002/nme.6237

Adaptive ACMS: A robust localized Approximated Component Mode Synthesis Method
preprint, January 2017

Madureira, Alexandre L.; Sarkis, Marcus
arXiv
DOI: 10.48550/arxiv.1709.04044

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

Abstract

Citation Formats

Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations: Adaptive BDDC algorithms for plane wave discretization journal, August 2018

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Adaptive ACMS: A robust localized Approximated Component Mode Synthesis Method preprint, January 2017

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journal, October 2019

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