Finite Element Methods for Maxwell's Transmission Eigenvalues

Iterative Methods for Transmission Eigenvalues

Transmission eigenvalues have important applications in inverse scattering theory. They can be used to obtain useful information of the physical properties, such as the index of refraction, of the scattering target. Despite considerable effort devoted to the existence and estimation for the transmission eigenvalues, the numerical treatment is limited. Since the problem is non-standard, classica...

Finite element methods for Maxwell's equations

Simulation and Experimental Study of Vibration and Noise of Pure Electric Bus Transmission based on Finite Element and Boundary Element Methods

Since the electric motor of pure electric vehicle replaced the engine, the "masking effect" disappears, and the problem of vibration and noise of the transmission becomes prominent. This is generated during the gear meshing and is transmitted to the housing through the shaft and bearing. Thereby, radiation noise of the housing are generated. The prediction and analysis...

Error Analysis for the Finite Element Approximation of Transmission Eigenvalues

In this paper we consider the transmission eigenvalue problem corresponding to acoustic scattering by a bounded isotropic inhomogeneous object in two dimensions. This is a non self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concerned with theoretical error analysis of a finite element method for computing the eigenvalues and corresponding eigenfunctions...

Lower Bounds for Eigenvalues of Elliptic Operators: By Nonconforming Finite Element Methods

The aim of the paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The general conclusion herein is that if local approximation properties of nonconforming finite element spaces Vh are better than global continuity properties of Vh, corresponding methods will produce lower bounds for eigenvalu...