Numerical Solution of Differential Equations in Irregular Plane Regions Using Quality Structured Convex Grids

TL;DR

This paper compares the accuracy of finite difference solutions on structured convex grids versus Delaunay-like triangulations for solving Poisson equations in irregular regions.

Contribution

It introduces a comparison between structured convex grids generated by variational methods and Delaunay triangulations for numerical solutions in irregular domains.

Findings

Structured convex grids yield accurate solutions for Poisson equations.

Comparison shows differences in accuracy between grid types.

Structured grids can be advantageous in irregular domain discretization.

Abstract

The variational grid generation method is a powerful tool for generating structured convex grids on irregular simply connected domains whose boundary is a polygonal Jordan curve. Several examples that show the accuracy of a difference approximation to the solution of a Poisson equation using these kind of structured grids have been recently reported. In this paper, we compare the accuracy of the numerical solution calculated by applying those structured grids with finite differences against the the solution obtained with Delaunay-like triangulations on irregular regions.