相关论文: Efficient numerical method of the fiber Bragg grat…

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational…

The demand for inverse design is increasing as the ability to fabricate sub-10 nm features expands the design space by orders of magnitude. Efficient inverse design benefits from differentiable models of light-structure interaction. While…

We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincar\'e-Steklov method. The method takes as input an unstructured, high-order quadrilateral mesh of…

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…

The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…

A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…

This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…

An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi operator expansion in terms of the Hamiltonian. The computational complexity is shown…

In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…

We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving…

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…

In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second order differential equations on a half-line. Our goal is to extend the classical resultss developed in the work of…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then…

We present a new method for the numerical solution of singular integral equations on the real axis. The method's value stems from an explicit formula for the Cauchy integral of a complex exponential multiplied by a rational function.…

It is well known that the choice of the iterative method is crucial in determining the speed of the converged solution. This article presents a detailed comparison between several iterative techniques for solving incmopressible…

In this paper, a non-polynomial spectral Petrov-Galerkin method and associated collocation method for substantial fractional differential equations (FDEs) are proposed, analyzed, and tested. We extend a class of generalized Laguerre…

This paper establishes and analyzes a second-order accurate numerical scheme for the nonlinear partial integrodifferential equation with a weakly singular kernel. In the time direction, we apply the Crank-Nicolson method for the time…

We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…

This study discusses a class of linear systems of fractional differential equations with non-constant coefficients, with a particular focus on problems exhibiting highly oscillatory and non-smooth behavior. We first establish the regularity…