A Derivative-Free Mesh Optimization Algorithm for Mesh Quality Improvement and Untangling

Figure 8

(a) Initial hydrocephalus mesh (zoomed-in). This mesh has a very skinny inverted element (red) with the element quality of 551.5212 enclosed by the red circle. (b) Optimized cylinder mesh (zoomed-in) using the proposed approach. The downhill simplex method is used to improve the worst element quality. After performing mesh optimization, all inverted elements are eliminated. (c) Optimized cylinder mesh (zoomed-in) using the traditional approach. The traditional approach focuses on improving the average element quality using the nonlinear conjugate gradient method. The optimized mesh does not have any inverted elements.

(a) Initial hydrocephalus mesh (zoomed-in)

(b) Optimized hydrocephalus using the proposed method (zoomed-in)

(c) Optimized cylinder mesh using the traditional method (zoomed-in)