Author: Shawn Daniel PautzPublisher:
ISBN:
Category :
Languages : en
Pages : 304
Book Description
Discrete Ordinates Transport Methods for Problems with Highly Forward-peaked Scattering
Author: Shawn Daniel PautzDiscrete Ordinates Transport Methods for Problems with Highly Forward-peaked Scattering
Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 162
Book Description
The author examines the solutions of the discrete ordinates (S{sub N}) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S{sub N} equations. This analysis shows that in this asymptotic limit the S{sub N} solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S{sub N} equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method.
Acceleration Techniques for Discrete-Ordinates Transport Methods with Highly Forward-Peaked Scattering
Author: Bruno Roger Fernand TurcksinPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
In this dissertation, advanced numerical methods for highly forward peaked scattering deterministic calculations are devised, implemented, and assessed. Since electrons interact with the surrounding environment through Coulomb interactions, the scattering kernel is highly forward-peaked. This bears the consequence that, with standard preconditioning, the standard Legendre expansion of the scattering kernel requires too many terms for the discretized equation to be solved efficiently using a deterministic method. The Diffusion Synthetic Acceleration (DSA), usually used to speed up the calculation when the scattering is weakly anisotropic, is inefficient for electron transport. This led Morel and Manteuffel to develop a one-dimensional angular multigrid (ANMG) which has proved to be very effective when the scattering is highly anisotropic. Later, Pautz et al. generalized this scheme to multidimensional geometries, but this method had to be stabilized by a diffusive filter that degrades the overall convergence of the iterative scheme. In this dissertation, we recast the multidimensional angular multigrid method without the filter as a preconditioner for a Krylov solver. This new method is stable independently of the anisotropy of the scattering and is increasingly more effective and efficient as the anisotropy increases compared to DSA preconditioning wrapped inside a Krylov solver. At the coarsest level of ANMG, a DSA step is needed. In this research, we use the Modified Interior Penalty (MIP) DSA. This DSA was shown to be always stable on triangular cells with isotropic scattering. Because this DSA discretization leads to symmetric definite-positive matrices, it is usually solved using a conjugate gradient preconditioned (CG) by SSOR but here, we show that algebraic multigrid methods are vastly superior than more common CG preconditioners such as SSOR. Another important part of this dissertation is dedicated to transport equation and diffusion solves on arbitrary polygonal meshes. The advantages of polygonal cells are that the number of unknowns needed to mesh a domain can be decreased and that adaptive mesh refinement implementation is simplified: rather than handling hanging nodes, the adapted computational mesh includes different types of polygons. Numerical examples are presented for arbitrary quadrilateral and polygonal grids. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148243
New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations
Author: Jacques TagoudjeuPublisher: Universal-Publishers
ISBN: 1599423960
Category : Mathematics
Languages : en
Pages : 161
Book Description
This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.
The Use of Computers in Radiation Therapy
Author: Wolfgang SchlegelPublisher: Springer Science & Business Media
ISBN: 3642597580
Category : Medical
Languages : en
Pages : 630
Book Description
Computers have had and will continue to have a tremendous impact on professional activity in almost all areas. This applies to radiological medicine and in particular to radiation therapy. This book compiles the most recent developments and results of the application of computers and computer science as presented at the XIIIth International Conference on the Use of Computers in Radiation Therapy in Heidelberg, Germany. The text of both oral presentations and posters is included. The book is intended for computer sientists, medical physicists, engineers and physicians in the field of radiation therapy and provides a comprehensive survey of the entire field.
Computational Methods in Transport
Author: Frank GrazianiPublisher: Springer Science & Business Media
ISBN: 3540281258
Category : Computers
Languages : en
Pages : 539
Book Description
Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.
Some Techniques to Evaluate the Scattering Source in the Discrete Ordinate Transport Equation with Highly Anisotropic Scattering
Author: Quazi SharfuddinPublisher:
ISBN:
Category : Scattering (Physics)
Languages : en
Pages : 146
Book Description
Light Scattering Reviews 2
Author: Alexander A. KokhanovskyPublisher: Springer Science & Business Media
ISBN: 3540684352
Category : Science
Languages : en
Pages : 366
Book Description
This book is to continue the Light Scattering Reviews series devoted to modern knowledge and milestones in both experimental and theoretical techniques related to light scattering and radiative transport problems. It gives a valuable picture of recent developments in the area of remote sensing and radiative transfer. The work has capabilities to further facilitate studes in light scattering media optics and be of importance for researchers across various scientific fields including astronomy, meterology and geophysics.
Studies in Application of Discrete Ordinates Transport Methods to Light Transport Calculations: Preparation of Mie Theory Cross Sections In Legendre Polynomials
Author: Duaine LindstromPublisher:
ISBN:
Category :
Languages : en
Pages : 115
Book Description
A study was performed to determine the applicability of discrete ordinates codes to the transport of light through particulates. Light is scattered with high anisotropy by particulates. This high anisotropy requires expansion in high Legendre order for accurate expression by discrete ordinates codes. Procedures for convenient and economical production of light scattering data (Mie theory) in discrete ordinates format were developed and tested. One-dimensional time-dependent discrete ordinates calculations were performed using the TDA (Time Dependent ANISN) code with a simple cloud model. Computer storage and time limitations are outlined. Extension to largest particle sizes and a second space dimension can best be accomplished using asymmetric discrete angle sets to conserve computer resources. Further economies might be accomplished by normalization of low-order data for problems dominated by multiple scattering. Relaxation of the need to express data in Legendre series could offer further economy, but may require significant development. (Author).
Author: