Domain Decomposition Approaches for PDE Based Mesh Generation
Adaptive, partial differential equation (PDE) based, mesh generators are introduced. The mesh PDE is typically coupled to the physical PDE of interest and one has to be careful not to introduce undue computational burden. Here we provide an overview of domain decomposition approaches to reduce this computational overhead and provide a parallel solver for the coupled PDEs. A preview of a new analysis for optimized Schwarz methods for the mesh generation problem using the theory of M-functions is given. We conclude by introducing a two-grid method with FAS correction for the grid generation problem.
I would like to thank my former students Alex Howse, Devin Grant, and Abu Sarker for their assistance and some of the plots included in this paper, and also Felix Kwok for several discussions related to this work.
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