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An A Posteriori Error Estimator for Adaptive Mesh Refinement Using Parallel In-Element Particle Tracking Methods

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High Performance Computing for Computational Science — VECPAR 2002 (VECPAR 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2565))

Abstract

Particle tracking methods are a versatile computational technique central to the simulation of a wide range of scientific applications. In this paper we present an a posteriori error estimator for adaptive mesh refinement (AMR) using particle tracking methods. The approach uses a parallel computing framework, the “in-element” particle tracking method, based on the assumption that particle trajectories are computed by problem data localized to individual elements. Adaptive mesh refinement is used to control the mesh discretization errors along computed characteristics of the particle trajectories. Traditional a posteriori error estimators for AMR methods inherit flaws from the discrete solution of time-marching partial differential equations (PDEs)-particularly for advection/convection-dominated transport applications. To address this problem we introduce a new a posteriori error estimator based on particle tracking methods.We present experimental results that detail the performance of a parallel implementation of this particle method approach for a two-dimensional, time-marching convection-diffusion benchmark problem on an unstructured, adaptive mesh.

This work was supported by NSF grants DGE-9987589 and ACI-9908057, DOE grant DG-FG02-99ER25373, and the Alfred P. Sloan Foundation.

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Author information

Authors and Affiliations

  1. Information Technology Laboratory, US Army Engineer and Research Development Center, 39180, Vicksburg, Mississippi

    Jing-Ru C. Cheng

  2. Department of Computer Science and Engineering, The Pennsylvania State University, University Park, 16802, PA, USA

    Paul E. Plassmann

Authors
  1. Jing-Ru C. Cheng
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  2. Paul E. Plassmann
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Editor information

Editors and Affiliations

  1. Faculdade de Engenharia da, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    José M. L. M. Palma  & A. Augusto Sousa  & 

  2. Department of Computer Science, University of Tennessee, 37996-1301, Knoxville, TN, USA

    Jack Dongarra

  3. Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera, s/n, Apartado 22012, 46020, Valencia, Spain

    Vicente Hernández

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© 2003 Springer-Verlag Berlin Heidelberg

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Cheng, JR.C., Plassmann, P.E. (2003). An A Posteriori Error Estimator for Adaptive Mesh Refinement Using Parallel In-Element Particle Tracking Methods. In: Palma, J.M.L.M., Sousa, A.A., Dongarra, J., Hernández, V. (eds) High Performance Computing for Computational Science — VECPAR 2002. VECPAR 2002. Lecture Notes in Computer Science, vol 2565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36569-9_7

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  • DOI: https://doi.org/10.1007/3-540-36569-9_7

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  • Print ISBN: 978-3-540-00852-1

  • Online ISBN: 978-3-540-36569-3

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