A numerical treatment for the Dirichlet boundary value problem on regular triangular grids for homogeneous Helmholtz equations is presented, which also applies to the convection-diffusion problems. The main characteristic of the method is that an accuracy estimate is provided in analytical form with a better evaluation than that obtained with the usual finite difference method. Besides, this cl...

In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second order accurate convex splitting scheme for the modified phase field crystal equation, a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case. The fully discrete, fully second order finite difference scheme in question was derived in a re...

In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β ∈ (1,2]. We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are ana...

This paper discusses a new computational scheme based on Functional Networks and applies it to the problem of classification and quantification of gas species in a mixture. A Generalized Functional Network as a new classifier is proposed in order to improve the potentialities of the standard Functional Network classifier. Both methodology and learning algorithm are derived. The performance of t...

This note presents an elementary numerical scheme for discretizing the Laplace-Beltrami operator on smooth manifolds, as a difference operator of arbitrary high order. The method is coordinate-free, and involves very little geometry.

We have characterized a class of spurious solutions that appears when using the finite difference method to solve the effective mass approximation equations. We find that the behavior of these solutions as predicted by our model shows excellent agreement with numerical results. Using this interpretation we find a set of analytical expressions for conditions that the Luttinger parameters must sa...

The thesis concentrates on the numerical analysis of electromagnetic fields with the finite difference method. Simple and fast approximative techniques are studied and developed for the estimation of the electromagnetic properties of various structures. Especially, techniques which preserve the simplicity of a structured lattice are explored. The emphasis in the thesis is put more into the rapi...

In this paper we describe a new finite-difference method (FDM) EEG forward problem formulation which accounts for anisotropy of the various head tissues in the volume conductor model of the head. Our proposal, being based on FDM, derives the head model directly from patient’s specific clinical images. We present here the numerical FD formulation and the comparison of the proposed method with a ...

In this paper we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods in complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficien...