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This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding…
We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a…
Chebyshev filtered subspace iteration is a well-known algorithm for the solution of (symmetric/Hermitian) algebraic eigenproblems which has been implemented in several application codes~\cite{Kronik:2006ff, abinit:2020} or in stand alone…
This paper introduces an approach to decoupling singularly perturbed boundary value problems for fourth-order ordinary differential equations that feature a small positive parameter $\epsilon$ multiplying the highest derivative. We…
We consider the computation of quadrature rules that are exact for a Chebyshev set of linearly independent functions on an interval $[a,b]$. A general theory of Chebyshev sets guarantees the existence of rules with a Gaussian property, in…
Two numerical methods are developed to reduce the solution of the radial Schr\"odinger equation for proposed heavy quark-antiquark interactions, into the solution of the eigenvalue problem for the infinite system of tridiagonal matrices.…
The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a harmonic point source. Its solution consists of a set of discrete modes radiating into the upper…
The calculation of a three-dimensional underwater acoustic field has always been a key problem in computational ocean acoustics. Traditionally, this solution is usually obtained by directly solving the acoustic Helmholtz equation using a…
We investigate the pseudospectrum of the Kerr black hole, which indicates the instability of the spectrum of quasinormal modes (QNMs) of the Kerr black hole. Methodologically, we use the hyperboloidal framework to cast the QNM problem into…
Spectral methods are now common in the solution of ordinary differential eigenvalue problems in a wide variety of fields, such as in the computation of black hole quasinormal modes. Most of these spectral codes are based on standard…
Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of…
Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit…
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
The authors consider the interior Dirichlet problem for Laplace's equation on planar domains with corners. In order to approximate the solution of the corresponding double layer boundary integral equation, they propose a numerical method of…
We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…
We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method which solves boundary value problems in complex domains by…
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the…