This week, Dr. Devina Sanjaya, an ANSLab partner, is presenting a paper at the American Institute for Aeronautics and Astronautics SciTech Forum on our collaborative work (mostly Devina’s work) on mesh adaptation for high-order finite-element methods, with applications in aerodynamics. The paper is titled “Error Sampling and Synthesis for High-Order Node Movement”; here’s a link, or see the ANSLab publications page. For a super-short summary, here’s the abstract:
This paper focuses on the error sampling and synthesis procedure within an optimization framework for high-order metric-based mesh adaptation in high-order finite-element (FEM) discretization. This mesh optimization framework is designed to handle arbitrary FEM discretization order, geometry order, and element types. In performing a metric-based adaptation, the framework uses a high-order Riemannian metric field to encode the curvature, anisotropy, and global coupling between vertices and high-order geometry nodes. An error model and a cost model are employed to iteratively construct the desired Reimannian metric field and guide a series of globally coupled vertex (r-adaptation) and high-order geometry (q-adaptation) node movements. The results mesh is an optimal high-order (curved) mesh that conforms to the specified metric field. The error model requires an error sampling and synthesis procedure, which involves several steps, including element splitting, random sampling of high-order geometry node movements, and estimating the metric-base error kernel on each mesh element. This paper aims to: 1) discuss the theoretical underpinnings of a robust, a posteriori, metric-based error model for qr-adaptation and 2) provide a status update on the 1D HOMES algorithm, wich is a native extensions of the Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm to a higher order.