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Title: Stencil computations for PDE-based applications with examples from DUNE and hypre

Abstract

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend the software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [2]
  1. Univ. of Munster, Munster (Germany)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1438745
Report Number(s):
LLNL-JRNL-681537
Journal ID: ISSN 1532-0626
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Concurrency and Computation. Practice and Experience
Additional Journal Information:
Journal Volume: 29; Journal Issue: 17; Journal ID: ISSN 1532-0626
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; stencil computations; partial differential equations

Citation Formats

Engwer, C., Falgout, R. D., and Yang, U. M. Stencil computations for PDE-based applications with examples from DUNE and hypre. United States: N. p., 2017. Web. doi:10.1002/cpe.4097.
Engwer, C., Falgout, R. D., & Yang, U. M. Stencil computations for PDE-based applications with examples from DUNE and hypre. United States. https://doi.org/10.1002/cpe.4097
Engwer, C., Falgout, R. D., and Yang, U. M. 2017. "Stencil computations for PDE-based applications with examples from DUNE and hypre". United States. https://doi.org/10.1002/cpe.4097. https://www.osti.gov/servlets/purl/1438745.
@article{osti_1438745,
title = {Stencil computations for PDE-based applications with examples from DUNE and hypre},
author = {Engwer, C. and Falgout, R. D. and Yang, U. M.},
abstractNote = {Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend the software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.},
doi = {10.1002/cpe.4097},
url = {https://www.osti.gov/biblio/1438745}, journal = {Concurrency and Computation. Practice and Experience},
issn = {1532-0626},
number = 17,
volume = 29,
place = {United States},
year = {2017},
month = {2}
}

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Works referenced in this record:

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Works referencing / citing this record:

Preparing sparse solvers for exascale computing
journal, January 2020

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