Updating Meshes On Deforming Domains: An Application Of The Target-Matrix Paradigm

A method for updating meshes in response to domain deformation is formulated within the target-matrix mesh optimization paradigm. By casting the problem within this paradigm, various formulations of the problem can be considered. Two local metrics are suggested for use in a multi-variable objective function to update meshes via numerical optimization. Both guarantee that if the deformation is null, the original mesh on the un-deformed domain will be replicated. Further, target matrices are constructed in a manner that ensures the updated mesh is as similar to the un-deformed mesh as possible. Numerical experiments confirm these properties on 2D examples. The update method has limitations, of course, the most important being that there is no guarantee that the deformed mesh will be invertible. Published in 2007 by John Wiley & Sons, Ltd.