Cost-effectiveness of fully implicit moving mesh adaptation: a practical investigation in 1D

  • Authors:

  • Giovanni Lapenta;Luis Chacón

  • Affiliations:

  • Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM;Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

The cost-effectiveness of moving mesh adaptation is studied in a number of 1D tests. We propose a method that is based on two established modern techniques. First, we use a moving mesh approach based on the classic equidistribution method. Second, we discretize the model equations for grid and physics using a conservative finite volume method and we solve the resulting equations with a preconditioned inexact Newton-Krylov method. Using these state of the art methods, we consider the question of whether a real improvement in performance can be achieved using adaptive grids. We consider rigorous metrics of the accuracy and cost of a numerical solution on uniform and adaptive grids. For a number of classic but challenging problems we demonstrate that indeed adaptive grids can lead to a great improvement in cost-effectiveness.