Domain decomposition parabolic Monge-Ampere approach for fast generation of adaptive moving meshes

A fast method is presented for adaptive moving mesh generation in multi-dimensions using a domain decomposition parabolic Monge-Ampere approach. The domain decomposition procedure employed here is non-iterative and involves splitting the computational domain into overlapping subdomains. An adaptive mesh on each subdomain is then computed as the image of the solution of the L-2 optimal mass transfer problem using a parabolic Monge-Ampere method. The domain decomposition approach allows straightforward implementation for the parallel computation of adaptive meshes which helps to reduce computational time significantly. Results are presented to show the numerical convergence of the domain decomposition solution to the single domain solution. Several numerical experiments are given to demonstrate the performance and efficiency of the proposed method. The numerical results indicate that the domain decomposition parabolic Monge-Ampere method is more efficient than the standard implementation of the parabolic Monge-Ampere method on the whole domain, in particular when computing adaptive meshes in three spatial dimensions. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a fast method for adaptive moving mesh generation in multi-dimensions using a domain decomposition parabolic Monge-Ampere approach. By computing an adaptive mesh on each subdomain and mapping the results to the solution of the L-2 optimal mass transfer problem, significant reduction in computational time and increased efficiency are achieved.