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

  • Jing-Ru C. Cheng
  • Paul E. Plassmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2565)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jing-Ru C. Cheng
    • 1
  • Paul E. Plassmann
    • 2
  1. 1.Information Technology LaboratoryUS Army Engineer and Research Development CenterVicksburg
  2. 2.Department of Computer Science and EngineeringThe Pennsylvania State UniversityUSA

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