Composite matrix construction for structured grid adaptive mesh refinement

Mark F. Adams; Stephen L. Cornford; Daniel F. Martin; Peter McCorquodale

doi:10.1016/j.cpc.2019.07.006

Composite matrix construction for structured grid adaptive mesh refinement

Mark F. Adams^*, Stephen L. Cornford, Daniel F. Martin, Peter McCorquodale

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

Abstract

Structured-grid adaptive mesh refinement (SAMR) is an approach to mesh generation that supports structured access to data and adaptive mesh refinement for discretized partial differential equations (PDEs). Solution algorithms often require that an inverse of an operator be applied, a system of algebraic equations must be solved, and this process is often the primary computational cost in an application. SAMR is well suited to geometric multigrid solvers, which can be effective, but often do not adapt well to complex geometry including material coefficients. Algebraic multigrid (AMG) is more robust in the face of complex geometry, in both boundary conditions and internal material interfaces. AMG requires a stored matrix linearization of the operator. We discuss an approach, and an implementation in the Chombo block-structured AMR framework, for constructing composite grid matrices from a SAMR hierarchy of grids for use in linear solvers in the PETSc numerical library. We consider a case study with the Chombo-based BISICLES ice sheet modeling application.

Original language	English
Pages (from-to)	35-39
Number of pages	5
Journal	Computer Physics Communications
Volume	244
DOIs	https://doi.org/10.1016/j.cpc.2019.07.006
Publication status	Published - Nov 2019

Bibliographical note

Funding Information:
This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute and the NUCLEI project under Contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory and the Director, Office of Science, Offices of Advanced Scientific Computing Research (ASCR) and Biological and Environmental Research (BER), of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, as a part of the ProSPect SciDAC Partnership. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Adaptive mesh refinement
Algebraic multigrid
PETSc
Preconditioning

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title = "Composite matrix construction for structured grid adaptive mesh refinement",

abstract = "Structured-grid adaptive mesh refinement (SAMR) is an approach to mesh generation that supports structured access to data and adaptive mesh refinement for discretized partial differential equations (PDEs). Solution algorithms often require that an inverse of an operator be applied, a system of algebraic equations must be solved, and this process is often the primary computational cost in an application. SAMR is well suited to geometric multigrid solvers, which can be effective, but often do not adapt well to complex geometry including material coefficients. Algebraic multigrid (AMG) is more robust in the face of complex geometry, in both boundary conditions and internal material interfaces. AMG requires a stored matrix linearization of the operator. We discuss an approach, and an implementation in the Chombo block-structured AMR framework, for constructing composite grid matrices from a SAMR hierarchy of grids for use in linear solvers in the PETSc numerical library. We consider a case study with the Chombo-based BISICLES ice sheet modeling application.",

keywords = "Adaptive mesh refinement, Algebraic multigrid, PETSc, Preconditioning",

author = "Adams, {Mark F.} and Cornford, {Stephen L.} and Martin, {Daniel F.} and Peter McCorquodale",

note = "Funding Information: This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute and the NUCLEI project under Contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory and the Director, Office of Science, Offices of Advanced Scientific Computing Research (ASCR) and Biological and Environmental Research (BER), of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, as a part of the ProSPect SciDAC Partnership. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = nov,

doi = "10.1016/j.cpc.2019.07.006",

language = "English",

volume = "244",

pages = "35--39",

journal = "Computer Physics Communications",

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AU - Adams, Mark F.

AU - Cornford, Stephen L.

AU - Martin, Daniel F.

AU - McCorquodale, Peter

N1 - Funding Information: This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute and the NUCLEI project under Contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory and the Director, Office of Science, Offices of Advanced Scientific Computing Research (ASCR) and Biological and Environmental Research (BER), of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, as a part of the ProSPect SciDAC Partnership. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Publisher Copyright: © 2019 Elsevier B.V.

PY - 2019/11

Y1 - 2019/11

N2 - Structured-grid adaptive mesh refinement (SAMR) is an approach to mesh generation that supports structured access to data and adaptive mesh refinement for discretized partial differential equations (PDEs). Solution algorithms often require that an inverse of an operator be applied, a system of algebraic equations must be solved, and this process is often the primary computational cost in an application. SAMR is well suited to geometric multigrid solvers, which can be effective, but often do not adapt well to complex geometry including material coefficients. Algebraic multigrid (AMG) is more robust in the face of complex geometry, in both boundary conditions and internal material interfaces. AMG requires a stored matrix linearization of the operator. We discuss an approach, and an implementation in the Chombo block-structured AMR framework, for constructing composite grid matrices from a SAMR hierarchy of grids for use in linear solvers in the PETSc numerical library. We consider a case study with the Chombo-based BISICLES ice sheet modeling application.

AB - Structured-grid adaptive mesh refinement (SAMR) is an approach to mesh generation that supports structured access to data and adaptive mesh refinement for discretized partial differential equations (PDEs). Solution algorithms often require that an inverse of an operator be applied, a system of algebraic equations must be solved, and this process is often the primary computational cost in an application. SAMR is well suited to geometric multigrid solvers, which can be effective, but often do not adapt well to complex geometry including material coefficients. Algebraic multigrid (AMG) is more robust in the face of complex geometry, in both boundary conditions and internal material interfaces. AMG requires a stored matrix linearization of the operator. We discuss an approach, and an implementation in the Chombo block-structured AMR framework, for constructing composite grid matrices from a SAMR hierarchy of grids for use in linear solvers in the PETSc numerical library. We consider a case study with the Chombo-based BISICLES ice sheet modeling application.

KW - Adaptive mesh refinement

KW - Algebraic multigrid

KW - PETSc

KW - Preconditioning

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DO - 10.1016/j.cpc.2019.07.006

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VL - 244

SP - 35

EP - 39

JO - Computer Physics Communications

JF - Computer Physics Communications

ER -

Composite matrix construction for structured grid adaptive mesh refinement

Abstract

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Keywords

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