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

Figure 5

These figures show the worst element quality and timing results to converge for various initial simplex diameters. A smaller value indicates a better element quality for the inverse mean ratio quality metric. In (a) and (b), the optimization problem does not converge when the initial simplex diameter is five. In (c) and (d), the optimization problem does not converge when the initial simplex diameter is five. In (e) and (f), all inverted elements are eliminated after optimization when the initial simplex diameters are 0.01 and 0.1. Other initial simplex diameters fail to eliminate inverted elements. In (g) and (h), the optimized meshes fail to untangle inverted elements when the initial simplex diameter is two and five.

(a) Cylinder mesh

(b) Cylinder mesh

(c) Bar mesh

(d) Bar mesh

(e) Hydrocephalus mesh

(f) Hydrocephalus mesh

(g) Airfoil mesh

(h) Airfoil mesh