The computation of guided modes in photonic crystal wave-guides is a key issue in the process of designing devices in photonic communications. Existing methods, such as the super-cell method, provide an efficient computation of well-confined modes. However, if the modes are not well-confined, the modelling error of the super-cell method becomes prohibitive and advanced methods applying transpar...

The Clenshaw Curtis method for numerical integration is extended to semiinfinite ([_0, 30] and infinite [-0% oc] intervals. The common framework for both these extensions and for integration on a finite interval is to (1) map the integration domain to tc[0, z], (2) compute a Fourier sine or cosine approximation to the transformd integrand via interpolation, and (3) integrate the approximation. ...

We give a new class of algorithms for computing sparsest shifts of a given polynomial. Our algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the early termination test. Through reformulating as multivariate shifts in a des...

In this paper we review some group theoretic techniques applied to discretizations of PDEs. Inspired by the recent years active research in Lie groupand exponential time integrators for differential equations, we will in the first part of the article present algorithms for computing matrix exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetri...

This paper presents a method to reduce the complexity of the deterministic maximum likelihood (DML) estimator in the wideband direction-of-arrival (WDOA) problem, which is based on interpolating the array projection matrix in the temporal frequency variable. It is shown that an accurate interpolator like Chebyshev’s is able to produce DML cost functions comprising just a few narrowband-like sum...