In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model – the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set ...

We investigate the application of a cell vertex nite volume discretization to multi-symplectic PDEs. The investigated discretization reduces to the Preissmann box scheme when used on a rectangular grid. Concerning arbitrary quadrilateral grids, we show that only methods with parallelogram-like nite volume cells lead to a multi-symplectic discretization, i.e., to a method that preserves a discre...

This paper is devoted to the discretization and numerical simulation of a new quantum drift-diffusion model that was recently derived. In a first step, we introduce an implicit semi-discretization in time which possesses some interesting properties: this system is well-posed, it preserves the positivity of the density, the total charge is conserved, and it is entropic (a free energy is dissipat...

Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivi...

Original scientific paper This paper presents semi-analytical solution for the problem of elastic impact of two beams. The solution is based on the finite element discretization of the structure and equation of motion solution using diagonalization method for solving a system of differential equations. This procedure avoids temporal discretization typical for numerical methods, and in this way ...

Explicit time discretizations of the Immersed Boundary method are known to require small timesteps to maintain stability. A number of implicit methods have been introduced to alleviate this restriction to allow for a more efficient method, but many of these methods still have a stability restriction on the timestep. Furthermore, almost no comparisons have appeared in the literature of the relat...

We extend previous results on the spectral distribution of discretization matrices arising from Bspline Isogeometric Analysis (IgA) approximations of a general d-dimensional second-order elliptic Partial Differential Equation (PDE) with variable coefficients. First, we provide the spectral symbol of the Galerkin B-spline IgA stiffness matrices, assuming only that the PDE coefficients belong to ...

Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection–diffusion problems have been proposed recently. These extensions are mostly based on probabilistic arguments and share the common feature of treating second-order operators in trace form, which makes them unsuitable...

Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : ∂ ∂t u j + ∇ · (a j u j) = ∇ · (D j ∇u j) + f j , These PDEs model a lot of important phenomena, see These PDEs model a lot o...

This paper deals with the numerical solution of a scalar nonlinear convection–diffusion equation. The space semi–discretization is carried out by the discontinuous Galerkin finite element method. Several possibilities of the time discretizations are discussed. To obtain a stable and efficient schemes we use implicit scheme for linear terms in combination with suitable explicit scheme for nonlin...