We investigate the behavior of five hyperbolic reaction-diffusion equations most commonly employed to describe systems of interacting organisms or reacting particles where dispersal displays inertia. We first discuss the macroscopic or mesoscopic foundation, or lack thereof, of these reaction-transport equations. This is followed by an analysis of the temporal evolution of spatially uniform sta...

This article presents a generalized B-spline surface subdivision scheme of arbitrary order with a tension parameter.We first propose a tensor-product subdivision scheme that produces ku×kv order generalized B-spline limit surfaces. Generalized B-spline surface is the unified and extended form of B-splines, trigonometric B-splines and hyperbolic B-splines (Fang et al. 2010). The tensor product s...

We report numerical performance of self-adaptive triangulation approach to improve numerical solutions of Poisson equations using bivariate spline functions. Starting with a uniform triangulation, we use the gradient values of an initial spline solution to generate an updated triangulation. Both refining and coarsening the initial triangulation are combined together and a global triangulation i...

Evolution of the main signal in a Lorentz dispersive medium is considered. The signal propagating in the medium is excited by a sine-modulated pulse signal, with its envelope described by a hyperbolic tangent function. Both uniform and non-uniform asymptotic representations for the signal are found. It is shown when the uniform representation can be reduced to the non-uniform one. The results o...

In this paper, a collocation finite difference scheme based on new cubic trigonometric B-spline is developed and analyzed for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with non-local conservation condition. The usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation functi...

This paper presents a generalization of Catmull-Clark-variant Doo-Sabin surfaces and non-uniform biquadratic B-spline surfaces called NURDSes (Non-Uniform Recursive Doo-Sabin Surfaces). One step of NURDS refinement can be factored into one non-uniform linear subdivision step plus one dual step. Compared to the prior non-uniform Doo-Sabin surfaces (i.e., quadratic NURSSes), NURDSes are convergen...

Interpolation of a sequence of points by spline curves generally requires the solution of a large system of equations. In this paper we provide a method which requires only local computation instead of a global system of equations and works for a large class of curves. This is a generalization of a method which previously developed for Bspline, NURBS and trigonometric CB-spline curves. Moreover...

In analysis of problems with parametric spline boundaries that are immersed or inserted into an underlying domain, the discretization on domain usually does not conform to boundaries. While fixed is great convenience as evolve, field approximations near require refinement in do quadrature cells. this paper, a kd-tree data structure together sign-based and/or distance-based strategy proposed for...

We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary twodimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize current l...