Generating Equidistributed Meshes in 2D via Domain Decomposition

TL;DR

This paper presents a method for generating 2D meshes using Schwarz domain decomposition combined with a local equidistribution principle, improving mesh quality through iterative nonlinear system solutions.

Contribution

It introduces the application of classical and optimized Schwarz domain decomposition methods to 2D mesh generation based on local equidistribution, with implementation details and numerical validation.

Findings

Effective mesh generation via domain decomposition

Improved convergence with optimized Schwarz methods

Numerical examples demonstrate approach performance

Abstract

In this paper we consider Schwarz domain decomposition applied to the generation of 2D spatial meshes by a local equidistribution principle. We briefly review the derivation of the local equidistribution principle and the appropriate choice of boundary conditions. We then introduce classical and optimized Schwarz domain decomposition methods to solve the resulting system of nonlinear equations. The implementation of these iterations are discussed, and we conclude with numerical examples to illustrate the performance of the approach.