In this paper, we articulate a meshless computational paradigm for the effective modeling, accurate physical simulation, and real-time animation of point-sampled solid objects. Both the interior and the boundary geometry of our volumetric object representation only consist of points, further extending the powerful and popular method of point-sampled surfaces to the volumetric setting. We build ...

The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite differ: ence and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the meth...

We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker–Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum-entropy Mn models. A realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closure. They ...

The fractal conservation law ∂tu + ∂x( f (u)) + (−∆)α/2u = 0 changes characteristics as α → 2 from non-local and weakly diffusive to local and strongly diffusive. In this paper we present a corrected finite difference quadrature method for (−∆)α/2 with α ∈ [0,2], combined with usual finite volume methods for the hyperbolic term, that automatically adjusts to this change and is uniformly converg...

We consider finite volume relaxation schemes for multidimensional scalar conservation laws. These schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of h1/4 in L∞([0, T ], Lloc(R d)) .