Non-oscillatory discretization methods based on the Local Extremum Diminishing principle, which were originally devised for compressible flow, are applied to the free-surface evolution equation. More specifically, both symmetric and upstream limited schemes are utilized in the calculation of the flow about the Series 60 hull, a naval frigate hull with sonar dome and transom stern, and a fully c...

The constructionof quadraticC 1 surfacesfrom B-spline control points is generalized to a wider class of control meshes capable of outlining arbitrary free-form surfaces in space. Irregular meshes with non quadrilateral cells and more or fewer than four cells meeting at a point are allowed so that arbitrary free-form surfaces with or without boundary can be modeled in the same conceptual frame w...

In this paper we consider the problem of computing the value and a supporting hyperplane of the convex envelope for quadratic and polynomial functions over polytopes with known vertex set. We show that for general quadratic functions the computation can be carried on through a copositive problem, but in some cases (including all the two-dimensional ones) we can solve a semidefinite problem. The...

We show that one can enumerate the vertices of convex hull integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, time polynomial dimension encoding size polytope. This extends a previous result by Artmann et al. who showed linear optimization such be done time.

We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. In [S. Kusiak and J. Sylvester, Comm. Pure Appl. Math., 56 (2003), pp. 1525–1548], we introduced the convex scattering support of a far field, a set which will be a subset of the convex hull of the support of any source ...

We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves earlier results in the literature. On the other hand we provide a polynomial-time algorithm to determine the hull number of planar partial cube quadrangulations. Inst...