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Discrete Surface Ricci Flow for General Surface Meshing in Computational Electromagnetics Using Iterative Adaptive Refinement

We propose a surface meshing approach for computational electromagnetics (CEM) based on discrete surface Ricci flow (DSRF) with iterative adaptive refinement (AR) in the parametric domain for the automated generation of high-quality surface meshes of arbitrary element type, order, and count. Surfaces are conformally mapped by DSRF to a canonical parametric domain, allowing a canonical seed mesh to be mapped back to an approximation of the original surface. The new DSRF-based meshing technique provides a framework for generation of meshes with high element quality, aimed to greatly enhance the accuracy, conditioning properties, stability, robustness, and efficiency of surface integral equation CEM solutions. We demonstrate the ability of the proposed DSRF technique to produce meshes with near-optimal element corner angles for complicated, highly varied surfaces such as the NASA almond and a fighter jet model, using triangular, quadrilateral, and discontinuous quadrilateral elements. Other element types are also discussed. Where high-fidelity meshing is desired, the technique can capture fine-scale detail using very few high-order elements. Where low-fidelity meshing is desired, DSRF with AR can accurately recreate course-scale detail using standard first-order elements (e.g., flat triangular patches).