On Mesh-to-Mesh Transfer Operators for Unstructured Multigrid Solvers

Abstract

A new mesh-to-mesh data transfer operator for unstructured multigrid methods is presented. The new algorithm integrates piecewise continuous (reconstructed) data deened on a source mesh over the control volumes of a target mesh. Analysis in one dimensions and numerical experiments in two dimensions demonstrate that this approach signiicantly reduces data transfer errors when compared to interpolation or agglomeration transfer algorithms, especially when transfering low-frequency data from coarse to ne meshes. It was expected that improved data transfer would translate into improved multigrid convergence rates. For Laplace's equation in one dimension, improvement of 10{15% was seen, while in two dimensions, improvement was about 2%. For the Euler equations in two dimensions, improvement in convergence rate was essentially zero. Possible reasons for this poor performance include insuucient coarse mesh convergence, the presence of high-frequency error modes, and subtle diierences in the implementation of multigrid schemes with diierent data transfer operators. All present indications are that improving mesh-to-mesh data transfer does not have nearly as signiicant an eeect on convergence rate as modest improvements in smoothing techniques on a single mesh. Even given the advanced state-of-the-art in smoothing techniques, that arena is expected to be a more fruitful one for future research .

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Cite this paper

@inproceedings{OllivierGooch2007OnMT, title={On Mesh-to-Mesh Transfer Operators for Unstructured Multigrid Solvers}, author={Carl Ollivier-Gooch}, year={2007} }