Related papers: Two Chebyshev Spectral Methods for Solving Normal …

This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…

We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a…

For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…

Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…

In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…

In this paper, two parallel methods for solving systems of accretive operator equations in Banach spaces are studied. The convergence analysis of the methods in both free-noise and noisy data cases is provided.

Using algebraic techniques we obtain quasinormal modes and frequencies associated to generalized forms of the scattering P\"oschl-Teller potential. This approach is based on the association of the corresponding equations of motion with…

In this paper, we present Gauss's law-preserving spectral methods and their efficient solution algorithms for curl-curl source and eigenvalue problems in two and three dimensions arising from Maxwell's equations. Arbitrary order…

We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which is…

We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…

We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is…

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…

We conjecture a new ordinary differential equation exactly isospectral to the radial component of the homogeneous Teukolsky equation. We find this novel relation by a hidden symmetry implied from a four-dimensional $\mathcal{N}=2$…

Here we obtain explicit formulae for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex…

We study the implementation of a Chebyshev spectral method with forward Euler integrator to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the…

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is…

Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of values rather than being just a fixed integer/fraction as it…

A Continuous Galerkin method-based approach is presented to compute the seismic normal modes of rotating planets. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core using a polynomial…

The paper presents a globally convergent algorithm for solving coefficient inverse problems. Being rooted in the globally convergent numerical method (SIAM J. Sci. Comput., 31, No.1 (2008), pp. 478-509) for solving multidimensional…

This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of…