We consider the problem of constructing spatial finite difference approximations on an arbitrary fixed grid which preserve any number of integrals of the partial differential equation and preserve some of its symmetries. A basis for the space of of such finite difference operators is constructed; most cases of interest involve a single such basis element. (The “Arakawa” Jacobian is such an elem...

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...

finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural finite element and boundary methods in structural introduction to finite element vibration analys...

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...

Particle finite element method (PFEM) is an effective numerical tool for solving large-deformation problems in geomechanics. By incorporating the node integration technique with strain smoothing into PFEM, we proposed smoothed particle (SPFEM). This paper extends SPFEM to three-dimensional cases and presents a executed on graphics processing units (GPUs) boost computational efficiency. The deta...