In this paper, we give an explicit method for mapping any simply connected surface onto the sphere in a manner which preserves angles. This technique relies on certain conformal mappings from differential geometry. Our method provides a new way to automatically assign texture coordinates to complex undulating surfaces. We demonstrate a finite element method that can be used to apply our mapping...

Qinghua Feng School of Science Shandong university of technology Zhangzhou Road 12#, Zibo , Shandong, 255049 China [email protected] Abstract: Based on the concept of decomposition, two alternating group explicit methods are constructed for 1D convection-diffusion equation with variable coefficient and 2D diffusion equations respectively. Both the two methods have the property of unconditional sta...

Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this paper we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise t...

In this paper, we consider a novel 3D visualization technique based on surface flattening for virtual colonoscopy. Such visualization methods could be important in virtual colonoscopy since they have the potential for non-invasively determining the presence of polyps and other pathologies. Further, we demonstrate a method which presents a surface scan of the entire colon as a cine, and affords ...

In this paper, an alternative approach for constructing an a posteriori error estimator for non-conforming approximation of scalar elliptic equation is introduced. The approach is based on the usage of post-processing conforming finite element approximation of the non-conforming solution . Then, the compatible a posteriori error estimator is defined by the local norms of difference between the ...

Fractional order partial differential equations, as generalizations of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of application. In this paper we discuss a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equation...

In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind fini...

Using classical finite difference schemes often generates numerical drawbacks such as spurious oscillations in the solution of the famous Black–Scholes partial differential equation. We analyze the fully implicit scheme, frequently used numerical method in Finance, that in the presence of discontinuous payoff and low volatility arises spurious oscillations. We propose a modification of this sch...