Abstract:
. Delaunay Triangulations with nonobtuse triangles at the boundaries satisfy a minimal requirement for Control Volume meshes. We motivate this quality requirement, discuss it in context with others that have been proposed, and give point placement strategies that generate the fewest or close to the fewest number of Steiner points needed to satisfy it for a particular problem instance. The advantage is that this strategy places a number of Steiner points proportional to the combinatorial size of the input rather than the local feature size, resulting in far fewer points in many cases. 1 Introduction Techniques for numerically approximating the solution to partial differential equations typically have at least three distinct phases: mesh generation, where the domain is partitioned into a finite number of pieces; discretization, which takes the mesh and derives a system of linear equations, Ax = b, whose solution can be used to obtain an approximation to a PDE over the domain; and ...
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