Spectral pollution
نویسنده
چکیده
M. PLUM Mathematisches Institut I, Universität Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe, Germany [Received on 10 December 2002; revised on 12 January 2004] It is well known that routine methods of computing the spectrum of a self-adjoint operator often lead to spurious eigenvalues in a gap between two parts of the essential spectrum. We provide a geometrical explanation for a numerical method of resolving this problem, and give some examples of its use.
منابع مشابه
Periodic Schrödinger Operators with Local Defects and Spectral Pollution
This article deals with the numerical calculation of eigenvalues of perturbed periodic Schrödinger operators located in spectral gaps. Such operators are encountered in the modeling of the electronic structure of crystals with local defects, and of photonic crystals. The usual finite element Galerkin approximation is known to give rise to spectral pollution. In this article, we give a precise d...
متن کاملEigenvalues in Spectral Gaps of Differential Operators
Spectral problems with band-gap spectral structure arise in numerous applications, including the study of crystalline structure and the determination of transmitted frequencies in photonic waveguides. Numerical discretization of these problems can result in spurious results, a phenomenon known as spectral pollution. We present a method for calculating eigenvalues in the gaps of self-adjoint ope...
متن کاملAirborne high spectral resolution lidar observation of pollution aerosol during EUCAARI-LONGREX
Airborne high spectral resolution lidar observations over Europe during the EUCAARI-LONGREX field experiment in May 2008 are analysed with respect to the optical properties of continental pollution aerosol. Continental pollution aerosol is characterized by its depolarisation and lidar ratio. Over all, the measurements of the lidar ratio and the particle linear depolarization ratio of pollution ...
متن کاملCarbon Leakage: The Role of Sequential Policy Setting
We analyze non-cooperative environmental policy when the only strategic interaction between countries is through bilateral transboundary pollution, i.e., countries are closed or small open economies. When countries set pollution taxes simultaneously, there is no carbon leakage. However, in the sequential-move game, the leader sets its pollution tax lower than the marginal damage from own pollut...
متن کاملDevelopment of remote sensing methods for assessment of heavy metal soil pollution near the city of Kajaran
Numerous ecological problems are based on the disturbance of natural equilibrium of chemical elements which finally brings to pollution of major environmental components. Among pollutants, priority is given particularly to the heavy metals (HM). A complex investigation of pollution of territories with HM implies application of diverse methods that include the assessment of the state of major co...
متن کاملA class of nonseparable and nonstationary spatial temporal covariance functions.
Spectral methods are powerful tools to study and model the dependency structure of spatial temporal processes. However, standard spectral approaches as well as geostatistical methods assume separability and stationarity of the covariance function; these can be very unrealistic assumptions in many settings. In this work, we introduce a general and flexible parametric class of spatial temporal co...
متن کامل