Louvain School of Engineering
Université catholique de Louvain, Belgium
"Optimizing the Geometrical Accuracy of 2D Curvilinear Finite Element Meshes"
The aim of this seminar is to present a method that enables to build geo- metrically accurate curvilinear meshes.
Consider a model entity G and the mesh entity M that is supposed to approximate G. The first questions to address are the following ones: how do we define a proper distance d(G,M) between G and M and how do we compute this distance efficiently? Two principal definitions for such distances have been proposed in the computational geometry literature, namely the Fréchet distance and the Hausdorff distance. In this paper, we present a way to accurately compute distances between a curvilinear finite element mesh and its underlying CAD.
Figure 1: Original straight-sided mesh (top left), unoptimized quadratic mesh with invalid elements (top right), valid quadratic mesh without geometrical ac- curacy optimization (bottom left), and geometrically optimized valid quadratic mesh (bottom right).
The next step is to minimize d(G,M) in order to obtain a valid and accurate high order mesh. Figure 1 shows different meshes of a NACA0012 wing where the optimization procedure was able to reduce the CAD-to-mesh distance by two orders of magnitude while maintaining a valid mesh.
The Shell Lectures in the Department of Computational and Applied Mathematics are made possible through the generous support of the Shell Oil Company and focus on topics related to the energy industry.