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A Condensed Constrained Nonconforming MortarBased Approach for Preconditioning Finite Element Discretization Problems
Abstract
This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation that is based on a proposed modified version of the mortar method. The wellknown mortar finite element discretization method is modified to admit a local structure, providing an elementbyelement or subdomainbysubdomain assembly property. This is achieved via the introduction of additional trace finite element spaces and degrees of freedom (unknowns) associated with the interfaces between adjacent elements or subdomains. The resulting nonconforming formulation and a reducedviastaticcondensation Schur complement form on the interfaces are used in the construction of auxiliary space preconditioners for a given conforming finite element discretization problem. Overall, the properties of these preconditioners are studied and their performance is illustrated on model second order scalar elliptic problems utilizing high order elements.
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Portland State Univ., OR (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1671181
 Report Number(s):
 LLNLJRNL798915
Journal ID: ISSN 10648275; 1001891
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 42; Journal Issue: 5; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; finite element method; auxiliary space; preconditioning; static condensation; mortar method; algebraic multigrid
Citation Formats
Kalchev, Delyan Z., and Vassilevski, Panayot. A Condensed Constrained Nonconforming MortarBased Approach for Preconditioning Finite Element Discretization Problems. United States: N. p., 2020.
Web. doi:10.1137/19m1305690.
Kalchev, Delyan Z., & Vassilevski, Panayot. A Condensed Constrained Nonconforming MortarBased Approach for Preconditioning Finite Element Discretization Problems. United States. doi:10.1137/19m1305690.
Kalchev, Delyan Z., and Vassilevski, Panayot. Wed .
"A Condensed Constrained Nonconforming MortarBased Approach for Preconditioning Finite Element Discretization Problems". United States. doi:10.1137/19m1305690.
@article{osti_1671181,
title = {A Condensed Constrained Nonconforming MortarBased Approach for Preconditioning Finite Element Discretization Problems},
author = {Kalchev, Delyan Z. and Vassilevski, Panayot},
abstractNote = {This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation that is based on a proposed modified version of the mortar method. The wellknown mortar finite element discretization method is modified to admit a local structure, providing an elementbyelement or subdomainbysubdomain assembly property. This is achieved via the introduction of additional trace finite element spaces and degrees of freedom (unknowns) associated with the interfaces between adjacent elements or subdomains. The resulting nonconforming formulation and a reducedviastaticcondensation Schur complement form on the interfaces are used in the construction of auxiliary space preconditioners for a given conforming finite element discretization problem. Overall, the properties of these preconditioners are studied and their performance is illustrated on model second order scalar elliptic problems utilizing high order elements.},
doi = {10.1137/19m1305690},
journal = {SIAM Journal on Scientific Computing},
number = 5,
volume = 42,
place = {United States},
year = {2020},
month = {10}
}