Towards Unstructured Mesh Generation Using the Inverse Poisson Problem

TL;DR

This paper introduces a novel method for generating unstructured quadrilateral meshes in planar domains by leveraging the inverse Poisson problem, resulting in nearly conformal grids with irregular vertices.

Contribution

It presents a new theoretical relation between mesh generation and the inverse Poisson problem, along with an algorithm to construct point-source distributions for mesh irregularities.

Findings

Successfully generates unstructured quadrilateral meshes with irregular vertices.

Produces nearly conformal grids away from irregular vertices.

Demonstrates the effectiveness of the inverse Poisson approach in mesh generation.

Abstract

A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical relation between the present problem, and the inverse Poisson (IP) problem with point sources. An IP algorithm is described, which constructs a point-source distribution, whose sources correspond to the irregular vertices of the mesh. Both the background theory and the IP algorithm address the global nature of the mesh generation problem. The IP algorithm is incorporated in a complete mesh generation scheme, which also includes an algorithm for creating the final mesh. Example results are presented and discussed.