Pseudospectral Time-Domain (PSTD) Methods for the Wave Equation: Realizing Boundary Conditions with Discrete Sine and Cosine Transforms

Discrete Cosine and Sine Transforms

The discrete fractional cosine and sine transforms

This paper is concerned with the definitions of the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST). The definitions of DFRCT and DFRST are based on the eigen decomposition of DCT and DST kernels. This is the same idea as that of the discrete fractional Fourier transform (DFRFT); the eigenvalue and eigenvector relationships between the DFRCT, DFRS...

A Pseudospectral Chebychev Method for the 2D Wave Equation with Domain Stretching and Absorbing Boundary Conditions

therefore the damping layer has to be large enough to prevent reentrant waves at the physical boundary. Hence In this paper we develop a method for the simulation of wave propagation on artificially bounded domains. The acoustic wave the approach is not only costly in terms of memory requireequation is solved at all points away from the boundaries by a ments but also it is not very flexible. In...

Numerical Absorbing Boundary Conditions Based on a Damped Wave Equation for Pseudospectral Time-Domain Acoustic Simulations

In the context of wave-like phenomena, Fourier pseudospectral time-domain (PSTD) algorithms are some of the most efficient time-domain numerical methods for engineering applications. One important drawback of these methods is the so-called Gibbs phenomenon. This error can be avoided by using absorbing boundary conditions (ABC) at the end of the simulations. However, there is an important lack o...

The discrete fractional random cosine and sine transforms

Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT. Numeral results of DFRNCT and DFRNST for one and two dimensional functions have been given.