This paper examines formulation of the discretization schemes for diffusion process simulation that allow coarse grid spacings in the areas of exponentially varying concentrations and fluxes. The method of integral identities is used as a common framework for exponential fitting of both the finite difference and finite element schemes. An exponentially fitted finite difference scheme, with disc...

background and aim of study: long span is seen in many clinical situations, treatment planning options of these cases are difficult and may require: fpd, rpd or isp. each option has its own disadvantages: mechanical, patient relief and cost respectively. this article will evaluate the stress distribution of another treatment option which is adding a single supporting implant to the fpd by using...

The celebrated Spectral Element Method (SEM) has appeared to be of great interest to extend the capabilities of spectral methods to complex geometries. However, using quadrangular (hexahedral in 3D) elements may be a severe restriction for the most complex geometries, because requiring a structured mesh. Thus, Finite element meshes are usually based on triangles (tetrahedra in 3D). Efforts have...

Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor-grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can b...

The design of interior cutouts in laminated composite panels is of great importance in aerospace, automobile and structural engineering. Based on the Tsai–Hill failure criterion of the first ply, this paper presents a newly developed Fixed (FG) Grid Evolutionary Structural Optimization (ESO) method to explore shape optimization of multiple cutouts in composite structures. Different design cases...

This paper details the development of the fixed grid FEA (FGFEA) method to the solution of eigenvalue (natural frequency and buckling) problems, using a 4 node 20 degree of freedom shell element. The formulation of the FG element stiffness, buckling and natural frequency equations is presented. The first natural frequency and buckling load are determined for the simply supported plate with a ce...

An efficient modification by Douglas and Kim of the usual alternating directions method reduces the splitting error from O(k2) to O(k3) in time step k. We prove convergence of this modified alternating directions procedure, for the usual non-mixed Galerkin finite element and finite difference cases, under the restriction that k/h2 is sufficiently small, where h is the grid spacing. This improve...