Related papers: Efficient Numerical Self-consistent Mean-field App…
We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e. unitarity, regime. The Bogoliubov-deGennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator, we explore the performance of algorithms for computing its…
Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…
It is shown that bound state solutions of the one dimensional Bogoliubov-de Gennes (BdG) equation may exist when the Fermi velocity becomes dependent on the space coordinate. The existence of bound states in continuum (BIC) like solutions…
Reaction-Diffusion equations can present solutions in the form of traveling waves. Such solutions evolve in different spatial and temporal scales and it is desired to construct numerical methods that can adopt a spatial refinement at…
Local polynomial smoothing is a widespread technique in data analysis, and Savitzky-Golay (SG) filters are one of its most well-known realizations. In real settings, the effectiveness of SG filtering depends critically on proper tuning of…
We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced…
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…
A novel method for calculating resonances in three-body Coulombic systems is proposed. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. The $e^- e^+ e^-$ S-state resonances up…
In April 2025 GMV announced a competition for finding the best method to solve a particular polynomial system over a finite field. In this paper we provide a method for solving the given equation system significantly faster than what is…
Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…
We present a stochastic method for solving the time-dependent Schr\"odinger equation, generalizing a ground-state full configuration interaction Quantum Monte Carlo method. By performing the time-integration in the complex plane close to…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the existence and uniqueness of solutions…
In this paper, we develop an efficient spectral-Galerkin-type search extension method (SGSEM) for finding multiple solutions to semilinear elliptic boundary value problems. This method constructs effective initial data for multiple…
This research addresses the numerical simulation of the Boltzmann transport equation for semiconductor devices by proposing a multidimensional self-adaptive numerical simulation framework. This framework is applied to two important…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and constant coefficients on the half line. Our method results in…