Automatic Generalized Quadrilateral Surface Meshing in Computational Electromagnetics by Discrete Surface Ricci Flow

We present methods for the automated generation of high-order generalized quadrilateral surface meshes for computational electromagnetics (CEM) using discrete surface Ricci flow and parametric domain iterative refinement. We offer a brief overview of discrete surface Ricci flow as it pertains to this work and demonstrate its usefulness for higher-order quadrilateral mesh generation. We present extremely-high-order surface meshes, automatically generated by this method using minute numbers of quadrilateral elements with exceptionally high geometrical orders, demonstrating the method's robustness on both simple and complicated surfaces. The examples of the NASA almond, one of the most popular benchmarking examples, and a more complicated fighter jet model, with as few as four elements of up to 50th geometrical order, are first of a kind, showing great promise for higher order CEM.