In this paper, we introduce the multi-domain hybrid Spectral-WENO method aimed at the
discontinuous solutions of hyperbolic conservation laws. The main idea is to conjugate the …

Any global or high order approximation method suffers from the Gibbs phenomenon if the
approximant has a jump discontinuity in the given domain. In this note, we present a …

Abstract Radial Basis Function (RBF) methods have become important tools for scattered
data interpolation and for solving partial differential equations (PDEs) in complexly shaped …

We discuss the use of Padé-Legendre interpolants as an approach for the postprocessing of
data contaminated by Gibbs oscillations. A fast interpolation based reconstruction is …

Spectral methods yield exponential convergence in the approximation of a globally smooth
function [3],[4],[13]. However, if the function has a local discontinuity such that the function is …

The multi-domain hybrid Spectral-WENO method (Hybrid) is introduced for the numerical
solution of two dimensional nonlinear hyperbolic systems in a Cartesian physical domain …

We describe Fourier pseudospectral time-domain simulations, carried out in order to study
light interacting with a metallic nanoscale object. The difficulty of using Fourier methods to …

HOW WELL DOES THE HERMITE–PADÉ APPROXIMATION SMOOTH THE GIBBS
PHENOMENON? 1. Introduction To reduce the Gibbs phenomenon exhi Page 1 …

Efficient Green's function (GF) evaluation in layered media is a holy grail of wave theory in
general and electromagnetics in particular. While there is a very large amount of knowledge …

Propagation of nonlinear strain waves through a layered composite material is considered.
The governing macroscopic wave equation for the long-wave case was obtained earlier by …