COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

Seminars

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Pre-Ostrom Seminar: Generating Good Meshes; Inverting Good Matrices

2004-01-14

4:10 p.m. Neill Hall 5W

Gilbert Strang

Abstract: An essential first step in many problems of numerical analysis and computer graphics is to cover a region with a reasonably regular mesh. We describe a short MATLAB code that defines the region by the distance d(x) to the boundary (with d < 0 inside the region). The algorithm decides the location of nodes and the choice of edges. At each iteration the mesh becomes a truss (with forces in the edges that move the nodes). Then the Delaunay algorithm resets the topology (the choice of edges). The input includes a size function h(x) to vary the desired meshlength over the region. The code and the ideas came from Per-Olof Persson. They extend directly to n dimensions. The 2D meshes are remarkably regular. In higher dimensions it is difficult to avoid