DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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 Laboratory (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:
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. Fri . "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},
journal = {Concurrency and Computation. Practice and Experience},
number = 17,
volume = 29,
place = {United States},
year = {Fri Feb 24 00:00:00 EST 2017},
month = {Fri Feb 24 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A Unified Sparse Matrix Data Format for Efficient General Sparse Matrix-Vector Multiplication on Modern Processors with Wide SIMD Units
journal, January 2014

  • Kreutzer, Moritz; Hager, Georg; Wellein, Gerhard
  • SIAM Journal on Scientific Computing, Vol. 36, Issue 5
  • DOI: 10.1137/130930352

Stencil computation optimization and auto-tuning on state-of-the-art multicore architectures
conference, November 2008

  • Datta, K.; Murphy, M.; Volkov, V.
  • 2008 SC - International Conference for High Performance Computing, Networking, Storage and Analysis
  • DOI: 10.1109/SC.2008.5222004

Parallel multigrid on hierarchical hybrid grids: a performance study on current high performance computing clusters: PARALLEL MULTIGRID ON HIERARCHICAL HYBRID GRIDS
journal, December 2012

  • Gmeiner, Björn; Köstler, Harald; Stürmer, Markus
  • Concurrency and Computation: Practice and Experience, Vol. 26, Issue 1
  • DOI: 10.1002/cpe.2968

A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE
journal, June 2008


A Local Support-Operators Diffusion Discretization Scheme for Quadrilateralr-zMeshes
journal, July 1998

  • Morel, J. E.; Roberts, Randy M.; Shashkov, Mikhail J.
  • Journal of Computational Physics, Vol. 144, Issue 1
  • DOI: 10.1006/jcph.1998.5981

A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework
journal, April 2008


A Massively Parallel Multigrid Method for Finite Elements
journal, November 2006

  • Bergen, B.; Gradl, T.; Hulsemann, F.
  • Computing in Science & Engineering, Vol. 8, Issue 6
  • DOI: 10.1109/MCSE.2006.102

The parallel execution of DO loops
journal, February 1974


Multicore-Optimized Wavefront Diamond Blocking for Optimizing Stencil Updates
journal, January 2015

  • Malas, T.; Hager, G.; Ltaief, H.
  • SIAM Journal on Scientific Computing, Vol. 37, Issue 4
  • DOI: 10.1137/140991133

A generic interface for parallel cell-based finite element operator application
journal, June 2012


A numerical solution of the Navier-Stokes equations using the finite element technique
journal, January 1973


Works referencing / citing this record:

Preparing sparse solvers for exascale computing
journal, January 2020

  • Anzt, Hartwig; Boman, Erik; Falgout, Rob
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2166
  • DOI: 10.1098/rsta.2019.0053