Towards Simulation-Driven Optimization of High-Order Meshes by the Target-Matrix Optimization Paradigm

We present a method for simulation-driven optimization of high-order curved meshes. This work builds on the results of Dobrev et al. (The target-matrix optimization paradigm for high-order meshes. ArXiv e-prints, 2018, https://​arxiv.​org/​abs/​1807.​09807), where we described a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of Knupp (Eng Comput 28(4):419–429, 2012). In contrast to Dobrev et al. (2018), where all targets were based strictly on geometric information, in this work we blend physical information into the high-order mesh optimization process. The construction of target-matrices is enhanced by using discrete fields of interest, e.g., proximity to a particular region. As these discrete fields are defined only with respect to the initial mesh, their values on the intermediate meshes (produced during the optimization process) must be computed. We present two approaches for obtaining values on the intermediate meshes, namely, interpolation in physical space, and advection remap on the intermediate meshes. Our algorithm allows high-order applications to have precise control over local mesh quality, while still improving the mesh globally. The benefits of the new high-order TMOP methods are illustrated on examples from a high-order arbitrary Lagrangian-Eulerian application (BLAST, High-order curvilinear finite elements for shock hydrodynamics. LLNL code, 2018, http://​www.​llnl.​gov/​CASC/​blast).