Shifted Laplacian multigrid for the elastic Helmholtz equation

The shifted Laplacian multigrid method is a well known approach for preconditioning the indefinite linear system arising from the discretization of the acoustic Helmholtz equation. This equation is used to model wave propagation in the frequency domain. However, in some cases the acoustic equation is not sufficient for modeling the physics of the wave propagation, and one has to consider the elastic Helmholtz equation. Such a case arises in geophysical seismic imaging applications, where the earth's subsurface is the elastic medium. The elastic Helmholtz equation is much harder to solve than its acoustic counterpart, partially because it is three times larger, and partially because it models more complicated physics. Despite this, there are very few solvers available for the elastic equation compared to the array of solvers that are available for the acoustic one. In this work we extend the shifted Laplacian approach to the elastic Helmholtz equation, by combining the complex shift idea with approaches for linear elasticity. We demonstrate the efficiency and properties of our solver using numerical experiments for problems with heterogeneous media in two and three dimensions

The Cosmic History of Black Hole Growth from Deep Multiwavelength Surveys

Significant progress has been made in the last few years on understanding how supermassive black holes form and grow. In this paper, we begin by reviewing the spectral signatures of Active Galactic Nuclei (AGN) ranging from radio to hard X-ray wavelengths. We then describe the most commonly used methods to find these sources, including optical/UV, radio, infrared and X-ray emission and optical emission lines. We then describe the main observational properties of the obscured and unobscured AGN population. Finally, we summarize the cosmic history of black hole accretion, i.e., when in the history of the Universe supermassive black holes were getting most of their mass. We finish with a summary of open questions and a description of planned and future observatories that are going to help answer them.Comment: 33 pages, 20 figures, review paper accepted for the Advances in Astronomy Special Issue "Seeking for the Leading Actor on the Cosmic Stage: Galaxies versus Supermassive Black Holes

The Evolution and Eddington Ratio Distribution of Compton Thick Active Galactic Nuclei

Previous studies of the active galactic nuclei (AGN) contribution to the cosmic X-ray background (CXB) consider only observable parameters such as luminosity and absorbing column. Here, for the first time, we extend the study of the CXB to physical parameters including the Eddington ratio of the sources and the black hole mass. In order to calculate the contribution to the CXB of AGN accreting at various Eddington ratios, an evolving Eddington ratio space density model is calculated. In particular, Compton thick (CT) AGN are modeled as accreting at specific, physically motivated Eddington ratios instead of as a simple extension of the Compton thin type 2 AGN population. Comparing against the observed CT AGN space densities and log N-log S relation indicates that CT AGN are likely a composite population of AGN made up of sources accreting either at >90% or <1% of their Eddington rate.Comment: accepted ApJ