This paper presents a continuous finite element method for solving the resonance line transfer pr... more This paper presents a continuous finite element method for solving the resonance line transfer problem in moving media. The algorithm is capable of dealing with three spatial dimensions, using hierarchically structured grids which are locally refined by means of duality-based a-posteriori error estimates. Application of the method to coherent isotropic scattering and complete redistribution gives a result of matrix structure which is discussed in the paper. The solution is obtained by way of an iterative procedure, which solves a succession of quasi-monochromatic radiative transfer problems. It is therefore immediately evident that any simulation of the extended frequency-dependent model requires a solution strategy for the elementary monochromatic transfer problem, which is fast as well as accurate. The present implementation is applicable to arbitrary model configurations with optical depths up to 10 3 -10 4 . Additionally, a combination of a discontinuous finite element method with a superior preconditioning method is presented, which is designed to overcome the extremely poor convergence properties of the linear solver for optically thick and highly scattering media. The contents of this article is as follows: * This work has been supported by the German Research Foundation (DFG) through SFB 359 (Project C2).
Introduction: The Radiation Field and its Transfer Equation
Numerical Methods in Multidimensional Radiative Transfer, 2009
ABSTRACT Light is important in many fields of science and technology (in addition to everyone&... more ABSTRACT Light is important in many fields of science and technology (in addition to everyone's daily life) because it can be used as an important tool for information and may provide significant amounts of energy and momentum. Although the complete description of light is extremely complicated (cf. Mandel and Wolf, 1995), it is often sufficient to characterize it just by the specific intensity, which is a function of position, direction and frequency (or wavelength), for details see Section 2. The main advantages of using specific intensities are (i) that they are comparatively easy to measure (observe) and (ii) that there exists a transport equation that allows the modeling from local quantities (as e.g. extinction coefficients, emissivities).
The article addresses the possibility of robust detection of geometrically small, low emission so... more The article addresses the possibility of robust detection of geometrically small, low emission sources on a significantly stronger background. This problem is important for homeland security. A technique of detecting such sources using Compton type cameras is developed, which is shown on numerical examples to have high sensitivity and specificity and also allows to assign confidence probabilities of the detection. 2D case is considered in detail.
We revisit [1] and re-interpret the main result therein. We prove that a sufficient condition for... more We revisit [1] and re-interpret the main result therein. We prove that a sufficient condition for the standard upwind DG approximation to converge to the correct limit solution in the diffusive regime is that the approximation space contains a linear space of continuous functions, and the restrictions of the functions of this space to each mesh cell contains the linear polynomials.
A finite element method for solving the monochromatic radiation transfer equation including scatt... more A finite element method for solving the monochromatic radiation transfer equation including scattering in three dimensions is presented. The algorithm employs unstructured grids which are adaptively refined. Adaptivity as well as ordinate parallelization reduce memory requirements and execution time and make it possible to calculate the radiation field across several length scales for objects with strong opacity gradients. An a posteriori error estimate for one particular quantity is obtained by solving the dual problem. The application to a sample of test problems reveals the properties of the implementation.
A preconditioner for monochromatic radiative transfer problems is presented. It is based on a smo... more A preconditioner for monochromatic radiative transfer problems is presented. It is based on a smoothing operator for specific intensities and a multi-level method for the Eddington approximation of the mean intensity. It is demonstrated that the method allows for fast solution of the discrete linear problems in the scattering dominant case as well as in transition regions.
The local discontinuous Galerkin methods for linear incompressible flow: A review
Abstract: In this paper, we review the development of the so-called localdiscontinuous Galerkin m... more Abstract: In this paper, we review the development of the so-called localdiscontinuous Galerkin method for linear incompressible uid ow. This isa stable, high-order accurate and locally conservativenite element methodwhose approximate solution is discontinuous across inter-element boundaries;this property renders the method ideally suited for hp-adaptivity. In the contextof the Oseen problem, we present the method and discuss its stability andconvergence properties.
... Corresponding author Email addresses: anahi@mate.unlp.edu.ar (Anahı Dello Russo ), ana@mate.u... more ... Corresponding author Email addresses: anahi@mate.unlp.edu.ar (Anahı Dello Russo ), ana@mate.unlp.edu.ar (Ana E. Alonso) 1Member of CIC, Provincia de Buenos Aires, Argentina. Preprint submitted to Elsevier November 4, 2010 Page 2. ...
This paper provides an overview of the new features of the finite element library deal.II version... more This paper provides an overview of the new features of the finite element library deal.II version 8.0.
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Papers by Guido Kanschat