相关论文: Numerical Method for Solving Obstacle Scattering P…

We model, simulate and control the guiding problem for a herd of evaders under the action of repulsive drivers. The problem is formulated in an optimal control framework, where the drivers (controls) aim to guide the evaders (states) to a…

We present a new algebraic method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. We applied a triangular wave set for the Marchenko equation kernel expansion in a separable form. The separable…

A system of linear integral equations is presented, which is the analog of the system of Marchenko integral equations, to solve the inverse scattering problem for the linear system associated with the derivative NLS equations. The…

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method…

A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of…

We investigate the use of stochastic methods for zero energy quantum scattering based on a path integral approach. With the application to the scattering of a projectile from a nuclear many body target in mind, we use the potential…

Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of…

This paper is concerned with the error estimation of the fast multipole method (FMM) for scattering problems in 2-D. The FMM error is caused by truncating Graf's addition theorem in each step of the algorithm, including two expansions and…

We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying…

We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…

A numerical approach to the problem of wave scattering by many small particles is developed under the assumptions k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. On the wavelength…

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…

The crew rostering problem (CRP) for pilots is a complex crew scheduling task assigning pairings, or sequences of flights starting and ending at the same airport, to pilots to create a monthly schedule. In this paper, we propose an…

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…

A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…

The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\Lambda$…

Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…

This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…

Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…