Improved Simultaneous Mesh Untangling and Quality Improvement Methods of 2D Triangular Meshes

Abstract

Few inverted or poor quality elements can ruin both the accuracy and efficiency of numerical solutions. This paper proposes improved mesh untangling and quality improvement methods using the modified mesh quality metric for 2D triangular meshes. The new mesh quality metric ensures highly inverted elements assign higher penalty when the signed area of the element is negative, and also produces more accurate signed areas for valid elements. Therefore, the proposed methods can quickly remove inverted elements and also improve worst element qualities compared with the existing methods. We also combine Delaunay-based edge flip with optimization-based mesh untangling and quality improvement methods to further improve worst element qualities. Numerical results show that the proposed methods yield better quality meshes for improvement of the worst quality and are faster than existing methods.