Related papers: Spectral methods on a triangle and W-systems
We propose a novel estimation procedure for certain spectral distributions associated with a class of high dimensional linear time series. The processes under consideration are of the form $X_t = \sum_{\ell=0}^\infty \mathbf{A}_\ell…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
A new concept, decomposition-unstable (DU) variety of a parametric polynomial system, is introduced in this paper and the stabilities of several triangular decomposition methods, such as characteristic set decomposition, relatively…
This paper investigates the stability properties of discrete-time multilinear dynamical systems via tensor spectral theory. In particular, if the dynamic tensor of a multilinear dynamical system is orthogonally decomposable (odeco), we can…
In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied…
We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…
In this paper we present a spectral collocation method for the fast evaluation of the Landau collision operator for plasma physics, which allows us to obtain spectrally accurate numerical solutions. The method is inspired by the seminal…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
We present a hybrid spectral element-Fourier spectral method for solving the coupled system of Navier-Stokes and Cahn-Hilliard equations to simulate wall-bounded two-phase flows in a three-dimensional domain which is homogeneous in at least…
We present a novel spectral method for the Allen-Cahn equation on spheres, eliminating the reliance on conventional quadrature exactness conditions. By replacing these conditions with a restricted isometry relation derived from…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…
This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution…
In this paper the salient features of the Plane Wave Expansion (PWE) method and the mixed variational technique are combined for the fast eigenvalue computations of arbitrarily complex phononic unit cells. This is done by expanding the…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
The computation of the symmetric regularized-long-wave (SRLW) equation, which describes weekly nonlinear ion acoustic and space-charge waves, is dealt with in this paper. The numerical scheme to be proposed applies the Fourier…
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
We study electromagnetic field propagation through an ideal, passive, triangular three-waveguide coupler using a symmetry based approach to take advantage of the underlying $SU(3)$ symmetry. The planar version of this platform has proven…