We compare several local absorbing boundary conditions for solving the Helmholtz equation, by a finite difference or finite element method, exterior to a general scatterer. These boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface. In order to compare the computational solution with an analytical solution, we consider, as an example, scattering about an...

The 3D Laplace equation is one of the important PDEs of physics and describes the phenomonology of electrostatics and magnetostatics. Frequently very precise solution of this PDE is required; but with conventional finite element or finite difference codes this is difficult to achieve because of the need for an exceedingly fine mesh which leads to often prohibitive CPU time. We present an altern...

The concept of topological sensitivity has been successfully employed as an imaging tool to obtain the correct initial topology and preliminary geometry of hidden obstacles for a variety of inverse scattering problems. In this paper, we extend these ideas to acoustic scattering involving transient waveforms and penetrable obstacles. Through a boundary integral equation framework, we present a d...

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...

The thin plate is a key structure in various musical instruments, including many percussion instruments and the soundboard of the piano, and also is the mechanism underlying electromechanical plate reverberation. As such, it is a suitable candidate for physical modelling approaches to audio effects and sound synthesis, such as finite difference methods—though great attention must be paid to the...

Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences (FDM) and lowest-order finite element methods (FEM). In this paper we confirm that a straightforward extension to higher-order finite element methods (hpFEM) in the classical sense is not possible. We formulate a weaker DNCP for the Poisson equation in one spatia...

The work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions. The approach makes use of the adaptive finite difference method presented by Huang and Sloan [SIAM J. Sci. Comput., 15 (1994), pp. 776–797]. This method is applied on a coarse grid to obtain a rough approximation of the so...

Abstract—Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with t...

An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a discretization studied earlier by H. B. Keller. Variable order is provided through deferred corrections, while a built-in natural asymptotic estimator is used to automatically refine the mesh in order...