Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

Kalchev, Delyan Z.; Vassilevski, Panayot S.

doi:10.1137/19M1286815

Title: Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

Abstract

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. Furthermore, these preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

Authors:

^[1]; Vassilevski, Panayot S. ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Portland State Univ., OR (United States)

Publication Date:: Thu Jun 11 00:00:00 EDT 2020

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

OSTI Identifier:: 1633520

Report Number(s):: LLNL-JRNL-788660
Journal ID: ISSN 1064-8275; 986694

Grant/Contract Number:: AC52-07NA27344; DMS-1619640

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing

Additional Journal Information:: Journal Volume: 42; Journal Issue: 3; 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; interior penalty; static condensation; algebraic multigrid

Citation Formats


                    Kalchev, Delyan Z., and Vassilevski, Panayot S. Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation.  United States: N. p., 2020. 
Web.  doi:10.1137/19M1286815.

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                    Kalchev, Delyan Z., & Vassilevski, Panayot S. Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation.  United States.  https://doi.org/10.1137/19M1286815

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                    Kalchev, Delyan Z., and Vassilevski, Panayot S. Thu .  
"Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation".  United States.  https://doi.org/10.1137/19M1286815.  https://www.osti.gov/servlets/purl/1633520.

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@article{osti_1633520,

  title        = {Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation},

  author       = {Kalchev, Delyan Z. and Vassilevski, Panayot S.},

  abstractNote = {We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. Furthermore, these preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.},

  doi          = {10.1137/19M1286815},

  journal      = {SIAM Journal on Scientific Computing},

  number       = 3,

  volume       = 42,

  place        = {United States},

  year         = {Thu Jun 11 00:00:00 EDT 2020},

  month        = {Thu Jun 11 00:00:00 EDT 2020}

}

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Works referenced in this record:

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Arnold, Douglas N.
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The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
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Title: Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

Abstract

Citation Formats

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