相关论文: Elastic interior transmission eigenvalues and thei…
The present paper proposes an inf-sup stable divergence free virtual element method and associated a priori, and a posteriori error analysis to approximate the eigenvalues and eigenfunctions of the Stokes spectral problem in one shot. For…
We investigate the passivity constraints on the relations between transmission, reflection, and absorption eigenvalues in linear time-invariant systems. Using techniques from matrix analysis, we derive necessary and sufficient conditions…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
We provide an analytical solution for the elastic fields in a two-dimensional unbounded isotropic body with a rigid inclusion. Our analysis is based on the boundary integral formulation of the elastostatic problem and geometric function…
Loss-induced transmission in waveguides, and reversed pump dependence in lasers, are two prominent examples of counter-intuitive effects in non-Hermitian systems with patterned gain and loss. By analyzing the eigenvalue dynamics of complex…
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…
In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
In this paper, we investigate two transmission eigenvalue problems associated with the scattering of a media with a coated boundary. In recent years, there has been a lot of interest in studying these eigenvalue problems. It can be shown…
We consider the transmission eigenvalues for a bounded scatterer with a periodically varying index of refraction, and derive the first order corrections to the limiting transmission eigenvalues. We assume the scatterer contrast to be of one…
This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…
In this paper, we analyze a virtual element method (VEM) for solving a non-selfadjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. We write a variational formulation and propose a $C^1$-conforming…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
A thorough backward stability analysis of Hotelling's deflation, an explicit external deflation procedure through low-rank updates for computing many eigenpairs of a symmetric matrix, is presented. Computable upper bounds of the loss of the…
We propose numerical algorithms for recovering parameters in eigenvalue problems for linear elasticity of transversely isotropic materials. Specifically, the algorithms are used to recover the elastic constants of a rotor core. Numerical…
In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…
In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete, if the electromagnetic parameters $\eps, \, \mu,…