Specific Shape Function Research Articles

Dislocation Dynamics in Semiconductor Thin Film-Substrate Systems

ABSTRACTA discrete dislocation dynamics model is developed to establish the equations of motion for three-dimensional interacting dislocation loops in the semiconductor thin film – substrate system. The film is assumed to be an elastic layer and is perfectly bonded with another elastic substrate. Dislocation loops are discretized into segments, each of which is represented by a parametric space curve of specific shape functions and associated degree of freedom. The dislocation stress field is calculated as an essential ingredient in the dislocation dynamics method. Dislocation dynamics and interaction with film surface/interface are simulated.

Green's Function Discretization Scheme for Sound Propagation in Nonuniform Flows

A new frequency-domain discretization technique that permits the numerical solution of the equation governing the propagation of small disturbances within nonuniform potential flows is described. The method can be applied successfully to the numerical solution of aeroacoustic problems because a good accuracy is preserved up to 3-4 points per period for three-dimensional unstructured meshes. The discretization scheme is based on a local interpolation formula that is strictly joined to the physics of wave propagation because It is constructed with the superimposition of elementary sources that are local solutions of the local convective wave equation. The method presents aspects in common with both finite difference and finite element methods, with the peculiarity that the local interpolation formula can be interpreted as a specific shape function introduced to take advantage of the physics of the problem. The method is applied to the potential equation linearized around an arbitrary aerodynamic mean flow, and several comparisons with theoretical results, as well as several convergence tests, are conducted to show that a good accuracy is preserved up to 3-4 points per period also for irregular meshes with both random and Systematic distortions. Numerical calculations are presented for three-dimensional problems with both uniform and nonuniform flow, and comparisons are made with theoretical and other available numerical results. With the appropriate generalizations, the method can be regarded as a new, efficient general approach for the discretization of generic partial differential equations.

VIBRATION OF RECTANGULAR PLATES USING PLATE CHARACTERISTIC FUNCTIONS AS SHAPE FUNCTIONS IN THE RAYLEIGH–RITZ METHOD

The plate characteristic functions are used to express the deflection shapes in the Rayleigh–Ritz method to study rectangular plate vibrations. Since the plate characteristic functions are reasonable approximations to the vibration modes, they are found to improve the convergence of vibration frequencies. These plate frequencies are used to check the accuracy of the Rayleigh frequencies associated with the plate characteristic function modes. Computations are carried out for each of the four mode categories of a clamped square plate. In each mode category, the first 30 natural frequencies are tabulated and the first nine mode diagrams are drawn. The results show that the choice of specific shape functions enhances the effectiveness of the Rayleigh–Ritz method.

Volume Rendering on Non-regular Grids

In this article we present the principle methods for volumerendering of non-regular grids as used in the Finite Element Method or the Method of Control Volumes. Besides linear element types, the methods discussed here also cover the handling of commonly used non-linear element types but little considered in the Computer Graphics community. The very basic operation in the whole rendering process, namely the interpolation of the geometry and function values is fully based on the element type specific shape functions, ensuring a consistent mathematical treatment of the object in the sense of the underlying numerical simulation. We discuss the implications of this approach and propose optimizations justified by general assumptions on the qualify of the simulation model.

Spurious modes of electromagnetic vector potential finite elements

The mode spectra of individual electromagnetic vector potential finite elements are studied in detail. Theoretical spectra are deduced from the general properties of vector fields and the specific shape functions used in particular elements. Results are compared with spectra calculated using standard isoparametric tetrahedron and hexahedron elements. It is shown that spurious shear modes are present in addition to the more familiar spurious divergence and translation modes. >