Related papers: On the Numerical Solution of the Near Field Refrac…

A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In such inverse problems, the functionals dampen or entirely…

This work addresses a central challenge in the numerical analysis of the cutoff spatially homogeneous Boltzmann equation: the development of rigorously justified, accurate numerical schemes. We present (i) a novel Fourier spectral method…

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…

In this paper, we develop a numerical method for determining the potential in one and two dimensional fractional Calder\'{o}n problems with a single measurement. Finite difference scheme is employed to discretize the fractional Laplacian,…

We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…

A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods…

This paper extends the algorithm schemes proposed in \cite{Nesterov2007a} and \cite{Nesterov2007b} to the minimization of the sum of a composite objective function and a convex function. Two proximal point-type schemes are provided and…

Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…

t is a known fact that near field diffraction or Fresnel diffraction calculations are difficult to perform exactly. It is in general necessary to make some approximations in order to obtain a more suitable form. In this work, a numerical…

For more than a century and a half it has been widely-believed (but was never rigorously shown) that the physics of diffraction imposes certain fundamental limits on the resolution of an optical system. However our understanding of what…

A known first order method to find a feasible solution to a conic problem is an adapted von Neumann algorithm. We improve the distance reduction step there by projecting onto the convex hull of previously generated points using a primal…

We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, produces a given illumination pattern on a target. Both…

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…

In this paper we investigate the problem of recovering the source term in an elliptic system from a measurement of the state on a part of the boundary. For the particular interest in reconstructing probably discontinuous sources, we use the…

In this paper, we will introduce a high order numerical method to solve the scattering problems with non-periodic incident fields and (locally perturbed) periodic surfaces. For the problems we are considering, the classical methods to treat…

The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by uniformly prox-regular sets. After obtaining well-posedness results, we propose a…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…