Related papers: A spectral projection method for transmission eige…
We analyze an approximate interior transmission eigenvalue problem in ${\mathbb R}^d$ for $d=2$ or $d=3$, motivated by the transmission problem of a transformation optics-based cloaking scheme and obtained by replacing the refractive index…
Spectral network identification aims at inferring the eigenvalues of the Laplacian matrix of a network from measurement data. This allows to capture global information on the network structure from local measurements at a few number of…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
We consider an inverse spectral theory in a domain with the cavity that is bounded by a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the solutions inside and outside the cavity. The ODE system is connected…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…
We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to approximate isolated eigenvalues. It is shown that entries…
This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel…
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication…
In this paper, we study the transmission eigenvalue problem for an anisotropic material with a conductive boundary. We prove that the transmission eigenvalues for this problem exist and are at most a discrete set. We also study the…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…
The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…
In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff--Love infinite plate problem.…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
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…
An application of the new formulation of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] to quantum scattering of Dirac particles from non-local separable potentials is presented. Eigenchannel vectors,…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
We explore a spectral initialization method that plays a central role in contemporary research on signal estimation in nonconvex scenarios. In a noiseless phase retrieval framework, we precisely analyze the method's performance in the…