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Title: A Condensed Constrained Nonconforming Mortar-Based 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 well-known mortar finite element discretization method is modified to admit a local structure, providing an element-by-element or subdomain-by-subdomain 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 reduced-via-static-condensation 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:
ORCiD logo [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  2. 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):
LLNL-JRNL-798915
Journal ID: ISSN 1064-8275; 1001891
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 42; Journal Issue: 5; Journal ID: ISSN 1064-8275
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 Mortar-Based 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 Mortar-Based Approach for Preconditioning Finite Element Discretization Problems. United States. doi:10.1137/19m1305690.
Kalchev, Delyan Z., and Vassilevski, Panayot. Wed . "A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems". United States. doi:10.1137/19m1305690.
@article{osti_1671181,
title = {A Condensed Constrained Nonconforming Mortar-Based 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 well-known mortar finite element discretization method is modified to admit a local structure, providing an element-by-element or subdomain-by-subdomain 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 reduced-via-static-condensation 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}
}

Journal Article:
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This content will become publicly available on October 7, 2021
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