We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to… (More)
A procedure for code Verification by the Method of Manufactured Solutions (MMS) is presented. Although the procedure requires a certain amount of creativity and skill, we show that MMS can be applied to a variety of engineering codes which numerically solve partial differential equations. This is illustrated by detailed examples from computational fluid… (More)
We solve the problem of generating a uniform Poisson-disk sampling that is both <b>maximal</b> and <b>unbiased</b> over bounded non-convex domains. To our knowledge this is the first provably correct algorithm with time and space dependent only on the number of points produced. Our method has two phases, both based on classical dart-throwing. The first… (More)
The Winslow equations from structured elliptic grid generation are adapted to smoothing of two-dimensional unstructured meshes using a finite difference approach. Winslow smoothing on unstructured quadrilateral meshes results in mesh folding less frequently than with traditional Laplacian smoothing.
We explore the notion of a Well-spaced Blue-noise Distribution (WBD) of points, which combines two desirable properties. First, the point distribution is random, as measured by its spectrum having blue noise. Second, it is well-spaced in the sense that the minimum separation distance between samples is large compared to the maximum coverage distance between… (More)
Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically… (More)