The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J...

In this paper, we describe a new hybrid method which combines the boundary element method (BEM) and the nite element method (FEM) to calculate the circuit models for layout dependent capacitances in VLSI circuits. The hybrid method which we present does more than solving a particular eld problem, it produces a good physical circuit model for the interface between the regions where the BEM and t...

In this paper an efficient analytical method is presented for calculating the eigenvalues of special matrices related to finite element meshes (FEMs) with regular topologies. In the proposed method, a skeleton graph is used as the model of a FEM. This graph is then considered as the Cartesian product of its generators. The eigenvalues of the Laplacian matrix of the entire graph are then easily ...

Many applications in biomedical engineering and surgical simulators require effective modeling methods for dynamic interactive simulations. Due to its high computation time, the standard Finite Element Method (FEM) cannot be used in such cases. A FEM-based method is first presented, which rely on the decomposition of the deformation of each element into a rigid motion and a pure deformation, an...

The Wave Based Method (WBM) is a deterministic prediction method. Due to its enhanced computational efficiency as compared to other deterministic prediction techniques for steady-state dynamic analysis such as the Finite Element Method (FEM), the WBM is applicable for problem analysis in the lowand midfrequency range. It has been shown already that the WBM is superior to the FEM for the predict...

This paper presents a comparison of numerical methods used to model large scale acoustic coupled fluidstructure interaction (FSI) problems for single and double-walled cylindrical shells. The finite element method (FEM) is used to model the structure while the fast multipole boundary element method (FMBEM) is used to model the fluid domain and both models are coupled on the shared boundary surf...

One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the ε-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to sta...

A fully discrete analysis of the finite element heterogeneous multiscale method (FEHMM) for elliptic problems with N + 1 well separated scales is discussed. The FEHMM is a numerical homogenization method that relies on macroscopic scheme (macro FEM) for the approximation of the effective solution corresponding to the multiscale problem. The effective data are recovered from micro scale computat...

In order to solve the elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured meshes, a nodal Discontinuous Galerkin Finite Element Method (DG-FEM) is presented, which combines the geometrical flexibility of the Finite Element Method and strongly nonlinear wave simulation capability of the Finite Volume Method. The equations of nonlinear elastody...

Radio-Frequency (RF) ablation is a minimally invasive method for treatment of primary and metastatic hepatic tumors. A catheter is introduced transcutaneously into the tumor, and tissue is heated up by application of radio-frequency current. In this work, I present the application of the Finite Element Method (FEM) for creating models of hepatic RF ablation to evaluate and improve catheter desi...