Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.

Effects of friction on the unconfined compressive response of articular cartilage: a finite element analysis.

Abstract: A finite element analysis is used to study a previously unresolved issue of the effects of platen-specimen friction on the response of the unconfined compression test; effects of platen permeability are also determined. The finite element formulation is based on the linear KLM biphasic model for articular cartilage and other hydrated soft tissues. A Galerkin weighted residual method is applied to both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via a penalty method. The solid phase displacements and fluid phase velocities are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problem of a cylindrical specimen of soft tissue in unconfined compression. These studies show that interfacial friction plays a major role in the unconfined compression response of articular cartilage specimens with small thickness to diameter ratios.

Numerical simulation of scattering from three-dimensional randomly rough surfaces

Abstract: Randomly rough surface patches in three dimensions are generated on the computer. The FD-TD method is used to compute scattering from surface patches by converting the Maxwell's equations into difference equations using a central difference approximation for the space and time derivatives. The volume of grids above the rough surface is divided into the total field and the scattered field regions. In between these two regions, obliquely incident waves are generated. To reduce computation, the volume of grids is chosen to be small, and a transformation is used to convert the scattered field into far zone fields for bistatic scattering coefficient calculations. Possible errors near the edge of the surface due to the use of a relatively small volume are suppressed by introducing a windowing function. Very good agreements are obtained between the results obtained by this method and those calculated by an integral equation method (IEM) for scattering from randomly rough perfectly conducting and dielectric surfaces. >

Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation

Abstract: We present an error analysis for an unconditionally energy stable, fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equa- tion, a modified Cahn-Hilliard equation coupled with the Darcy flow law. The scheme, proposed by S. M. Wise, is based on the idea of convex splitting. In this paper, we rigorously prove first order convergence in time and second or- der convergence in space. Instead of the (discrete)L ∞ (0,T;L 2 )∩L 2 (0,T;H 2 h ) error estimate, which would represent the typical approach, we provide a dis- creteL ∞ (0,T;H 1 )∩L 2 (0,T;H 3 h )e rror estimate for the phase variable, which allows us to treat the nonlinear convection term in a straightforward way. Our convergence is unconditionalin the sense that the time stepsis in no way constrained by the mesh spacingh .T his is accomplished with the help of anL 2 (0,T;H 3 h ) bound of the numerical approximation of the phase variable. To facilitate both the stability and convergence analyses, we establish a finite difference analog of a Gagliardo-Nirenberg type inequality.