This paper is concerned with a numerical method for multiscale elliptic problems. Using the framework of the Heterogeneous Multiscale Methods (HMM), we propose a micro-macro approache which combines finite element method (FEM) for the macroscopic solver and the pseudospectral method for the micro solver. Unlike the micro-macro methods based on standard FEM proposed so far in HMM we obtain, for ...

A method for computing highly accurate numerical solutions of 1D convection–diffusion equations is proposed. In this method, the equation is first discretized with respect to the spatial variable, transforming the original problem into a set of ordinary differential equations, and then the resulting system is integrated in time by the fourth-order Runge–Kutta method. Spatial discretization is d...

The analysis and solution of wave equations with absorbing boundary conditions by using a related first order hyperbolic system has become increasingly popular in recent years. At variance with several methods which rely on this transformation, we propose an alternative method in which such hyperbolic system is not used. The method consists of approximation of spatial derivatives by the Chebysh...

The propagation of arbitrary amplitude dust ion acoustic waves (DIAWs) in a magnetized collisional dusty plasma including hot electrons, with kappa velocity distribution for electrons, warm ions and dust particles has been studied. In the presence of immobile massive dust particulates, DIAWs have been investigated through the Sagdeev pseudo-potential method. It is demonstrated that the amplitud...

The Geophysical High Order Suite for Turbulence (GHOST) is a highly scalable Fortran 90-95 pseudo–spectral code that solves a variety of PDEs that are often encountered in turbulence studies. The use of pseudo–spectral methods has a long and distinguished history in the turbulence community that hardly needs expounding upon. The numerics employ a GalerkinFourier spectral method and nonlinear te...

In this paper, we propose a pseudo-spectral multiscale method for simulating complex systems with more than one spatial scale. Using a spectral decomposition, we split the displacement into its mean and fluctuation parts. Under the assumption of localized nonlinear fluctuations, we separate the domain into an MD (Molecular Dynamics) subdomain and an MC (MacrosCopic) subdomain. An interfacial co...

We present a novel method for generating additional pseudo-articulator trajectories suitable for use within the framework of a stochastically trained speech production system recently developed at CUED. The system is initialised by inverting a codebook of (articulator, spectral vector) pairs, and the target positions for a set of pseudo-articulators and the mapping from these to speech spectral...