Research Article

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

Figure 7

(a) Initial cylinder mesh (zoomed-in). This mesh has a very skinny element (red) with the element quality of 678.9248 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. The worst quality element has the worst element quality with 3.73. (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 worst quality element has the worst element quality with 8.23.
(a) Initial cylinder mesh (zoomed-in)
(b) Optimized cylinder mesh using downhill simplex method (zoomed-in)
(c) Optimized cylinder mesh using traditional method (zoomed-in)