Related papers: Finite element and integral equation methods to co…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…
Consider the scattering of a time-harmonic electromagnetic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper concerns the numerical solutions of the open cavity…
A finite element approach to solve numerically the Takagi-Taupin equations expressed in a weak form is presented and applied to simulate X-ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect…
We present and analyze an integral equation method for the scattering of a non-periodic source from a geometry consisting of two semi-infinite, periodic structures glued together in two dimensions. The two structures may involve a periodic…
We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic game theory and optimal control and show uniform convergence…
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complementing boundary condition to establish rigorous a priori…
A method is presented to investigate diffraction of an electromagnetic plane wave by an infinitely thin infinitely conducting circular cylinder with longitudinal slots. It is based on the use of the combined boundary conditions method that…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
This study presents a finite difference method (FDM) to model the electromagnetic field propagation in eccentric coaxial waveguides filled with lossy uniaxially anisotropic media. The formulation utilizes conformal transformation to map the…
This work presents the implementation, numerical examples and experimental convergence study of first- and second-order optimization methods applied to one-dimensional periodic gratings. Through boundary integral equations and shape…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…