Composite matrix construction for structured grid adaptive mesh refinement

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

doi:10.1016/j.cpc.2019.07.006

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.

Authors:

Adams, Mark F. ^[1]; Cornford, Stephen L. ^[2]; Martin, Daniel F. ^[1]; McCorquodale, Peter ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Swansea Univ., Swansea (United Kingdom)

Publication Date:: Tue Jul 23 00:00:00 EDT 2019

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Biological and Environmental Research (BER)

OSTI Identifier:: 1560616

Alternate Identifier(s):: OSTI ID: 1562588

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Computer Physics Communications

Additional Journal Information:: Journal Volume: 244; Journal Issue: C; Journal ID: ISSN 0010-4655

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Algebraic multigrid; Preconditioning; PETSc; Adaptive mesh refinement

Citation Formats


                    Adams, Mark F., Cornford, Stephen L., Martin, Daniel F., and McCorquodale, Peter. Composite matrix construction for structured grid adaptive mesh refinement.  United States: N. p., 2019. 
Web.  doi:10.1016/j.cpc.2019.07.006.

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                    Adams, Mark F., Cornford, Stephen L., Martin, Daniel F., & McCorquodale, Peter. Composite matrix construction for structured grid adaptive mesh refinement.  United States.  https://doi.org/10.1016/j.cpc.2019.07.006

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                    Adams, Mark F., Cornford, Stephen L., Martin, Daniel F., and McCorquodale, Peter. Tue .  
"Composite matrix construction for structured grid adaptive mesh refinement".  United States.  https://doi.org/10.1016/j.cpc.2019.07.006.  https://www.osti.gov/servlets/purl/1560616.

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@article{osti_1560616,

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

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

  abstractNote = {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.},

  doi          = {10.1016/j.cpc.2019.07.006},

  journal      = {Computer Physics Communications},

  number       = C,

  volume       = 244,

  place        = {United States},

  year         = {Tue Jul 23 00:00:00 EDT 2019},

  month        = {Tue Jul 23 00:00:00 EDT 2019}

}

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Figure 1: Diagram of stencil transformations: generic 5-point stencil (top left); boundary ghost cell reference removed (top right); coarse-fine ghost cell reference removed (bottom left); fine-coarse covered cell reference removed (bottom right)

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