Comparison of Algorithms for High-Order, Metric-Based Mesh Optimization
Devina P. Sanjaya, Krzysztof J. Fidkowski, Scott M. Murman · AIAA Scitech 2020 Forum · 2020
We assess the performance of two iterative mesh optimization algorithms for generating high-order, metric-conforming meshes appropriate for use with high-order, finite-element methods. The three key steps in these metric-based approaches are: 1) obtain the desired high-order, Riemannian metric field, 2) generate a linear, metric-conforming mesh, and 3) place the high-order geometry nodes such that the mesh-implied metric conforms to the desired metric field. The procedure to obtain the desired high-order metric field is similar to the Mesh Optimization via Error Sampling and Synthesis (MOESS) developed by Yano[1] for linear meshes. In this work, we consider two approaches to obtain the desired, higher-order metric field: 1) performing MOESS on a refined mesh, and 2) extending native MOESS to high-order MOESS (HOMES). The mesh regeneration procedures used to obtain the metric-conforming property are also described in detail. The accuracy benefits offered by these two proposed algorithms are presented for a series of one-dimensional problems. A two-dimensional proof of concept is also provided to establish the value of extending the proposed metric-based optimization algorithm to higher dimensions and to demonstrate the feasibility of the proposed mesh regeneration procedure in higher dimensions.