High-Order Metric Interpolation for Curved R-Adaption by Distortion Minimization

We detail how to use Newton’s method for distortion-based curved r-adaption to a discrete high-order metric field. To this end, we consider three existent ingredients. First, a specific-purpose solver for distortion minimization. Second, a log-Euclidean high-order metric interpolation. Third, a point localization procedure for curved high-order meshes. We also extend to discrete metric fields a distortion-based curved r-adaption framework. To extend the framework, we provide, for the log-Euclidean high-order metric interpolation, the first and second derivatives in physical coordinates. These derivatives are required by Newton’s method to solve the distortion minimization. The distortion minimization allows properly matching the anisotropic curved features of a discrete high-order metric. This matching capability might be relevant in global and cavity-based curved (straight-edged) high-order mesh adaption.