| An a posteriori error estimator for adaptive mesh refinement using parallel in-element particle tracking methods |
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| Jing-Ru Cheng - Department of Computer Science and Engineering, The Pennsylvania State University Paul Plassmann - Department of Computer Science and Engineering, The Pennsylvania State University |
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 \emph{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 \emph{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 \emph{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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