Optimal Point Placement for Mesh Smoothing

TL;DR

This paper presents efficient algorithms for optimizing vertex placement in unstructured meshes to improve element shapes, utilizing linear programming techniques and addressing problems beyond this framework.

Contribution

It introduces linear-time algorithms for mesh smoothing problems, including those not solvable by generalized linear programming, advancing mesh optimization methods.

Findings

Many mesh smoothing problems can be solved in linear time.

Efficient algorithms are provided for problems outside the generalized linear programming scope.

The methods improve shape quality in unstructured meshes.

Abstract

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into the generalized linear programming paradigm.