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Author: Publisher: ISBN: Category : Languages : en Pages : 7
Book Description
Numerous variance reduction techniques, such as splitting/Russian roulette, weight windows, and the exponential transform exist for improving the efficiency of Monte Carlo transport calculations. Typically, however, these methods, while reducing the variance in the problem area of interest tend to increase the variance in other, presumably less important, regions. As such, these methods tend to be not as effective in Monte Carlo calculations which require the minimization of the variance everywhere. Recently, ''Local'' Exponential Transform (LET) methods have been developed as a means of approximating the zero-variance solution. A numerical solution to the adjoint diffusion equation is used, along with an exponential representation of the adjoint flux in each cell, to determine ''local'' biasing parameters. These parameters are then used to bias the forward Monte Carlo transport calculation in a manner similar to the conventional exponential transform, but such that the transform parameters are now local in space and energy, not global. Results have shown that the Local Exponential Transform often offers a significant improvement over conventional geometry splitting/Russian roulette with weight windows. Since the biasing parameters for the Local Exponential Transform were determined from a low-order solution to the adjoint transport problem, the LET has been applied in problems where it was desirable to minimize the variance in a detector region. The purpose of this paper is to show that by basing the LET method upon a low-order solution to the forward transport problem, one can instead obtain biasing parameters which will minimize the maximum variance in a Monte Carlo transport calculation.
Author: Publisher: ISBN: Category : Languages : en Pages : 7
Book Description
Numerous variance reduction techniques, such as splitting/Russian roulette, weight windows, and the exponential transform exist for improving the efficiency of Monte Carlo transport calculations. Typically, however, these methods, while reducing the variance in the problem area of interest tend to increase the variance in other, presumably less important, regions. As such, these methods tend to be not as effective in Monte Carlo calculations which require the minimization of the variance everywhere. Recently, ''Local'' Exponential Transform (LET) methods have been developed as a means of approximating the zero-variance solution. A numerical solution to the adjoint diffusion equation is used, along with an exponential representation of the adjoint flux in each cell, to determine ''local'' biasing parameters. These parameters are then used to bias the forward Monte Carlo transport calculation in a manner similar to the conventional exponential transform, but such that the transform parameters are now local in space and energy, not global. Results have shown that the Local Exponential Transform often offers a significant improvement over conventional geometry splitting/Russian roulette with weight windows. Since the biasing parameters for the Local Exponential Transform were determined from a low-order solution to the adjoint transport problem, the LET has been applied in problems where it was desirable to minimize the variance in a detector region. The purpose of this paper is to show that by basing the LET method upon a low-order solution to the forward transport problem, one can instead obtain biasing parameters which will minimize the maximum variance in a Monte Carlo transport calculation.
Author: Publisher: ISBN: Category : Languages : en Pages : 110
Book Description
The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditional Monte Carlo simulation of r̀̀eal ̀̀particles. He refers to the resulting variance reduction method as the Local Importance Function Transform (LIFI) method. He demonstrates the efficiency of the LIFT method for several 3-D, linearly anisotropic scattering, one-group, and multigroup problems. In these problems the LIFT method is shown to be more efficient than the AVATAR scheme, which is one of the best variance reduction techniques currently available in a state-of-the-art Monte Carlo code. For most of the problems considered, the LIFT method produces higher figures of merit than AVATAR, even when the LIFT method is used as a b̀̀lack box.̀̀ There are some problems that cause trouble for most variance reduction techniques, and the LIFT method is no exception. For example, the author demonstrates that problems with voids, or low density regions, can cause a reduction in the efficiency of the LIFT method. However, the LIFT method still performs better than survival biasing and AVATAR in these difficult cases.
Author: Stephen A. Dupree Publisher: Springer Science & Business Media ISBN: 9780306467486 Category : Mathematics Languages : en Pages : 370
Book Description
The mathematical technique of Monte Carlo, as applied to the transport of sub-atomic particles, has been described in numerous reports and books since its formal development in the 1940s. Most of these instructional efforts have been directed either at the mathematical basis of the technique or at its practical application as embodied in the several large, formal computer codes available for performing Monte Carlo transport calculations. This book attempts to fill what appears to be a gap in this Monte Carlo literature between the mathematics and the software. Thus, while the mathematical basis for Monte Carlo transport is covered in some detail, emphasis is placed on the application of the technique to the solution of practical radiation transport problems. This is done by using the PC as the basic teaching tool. This book assumes the reader has a knowledge of integral calculus, neutron transport theory, and Fortran programming. It also assumes the reader has available a PC with a Fortran compiler. Any PC of reasonable size should be adequate to reproduce the examples or solve the exercises contained herein. The authors believe it is important for the reader to execute these examples and exercises, and by doing so to become accomplished at preparing appropriate software for solving radiation transport problems using Monte Carlo. The step from the software described in this book to the use of production Monte Carlo codes should be straightforward.
Author: Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
Global deep-penetration transport problems are difficult to solve using traditional Monte Carlo techniques. In these problems, the scalar flux distribution is desired at all points in the spatial domain (global nature), and the scalar flux typically drops by several orders of magnitude across the problem (deep-penetration nature). As a result, few particle histories may reach certain regions of the domain, producing a relatively large variance in tallies in those regions. Implicit capture (also known as survival biasing or absorption suppression) can be used to increase the efficiency of the Monte Carlo transport algorithm to some degree. A hybrid Monte Carlo-deterministic technique has previously been developed by Cooper and Larsen to reduce variance in global problems by distributing particles more evenly throughout the spatial domain. This hybrid method uses an approximate deterministic estimate of the forward scalar flux distribution to automatically generate weight windows for the Monte Carlo transport simulation, avoiding the necessity for the code user to specify the weight window parameters. In a binary stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media is to use the atomic mix (AM) approximation in which the transport problem is solved using ensemble-averaged material properties. The most ubiquitous deterministic model developed specifically for solving binary stochastic media transport problems is the Levermore-Pomraning (L-P) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the Levermore-Pomraning equations and another Monte Carlo algorithm (Algorithm B) that is more accurate as a result of improved local material realization modeling. Recent benchmark studies have shown that Algorithm B is often significantly more accurate than Algorithm A (and therefore the L-P model) for deep penetration problems such as examined in this paper. In this research, we investigate the application of a variant of the hybrid Monte Carlo-deterministic method proposed by Cooper and Larsen to global deep penetration problems involving binary stochastic media. To our knowledge, hybrid Monte Carlo-deterministic methods have not previously been applied to problems involving a stochastic medium. We investigate two approaches for computing the approximate deterministic estimate of the forward scalar flux distribution used to automatically generate the weight windows. The first approach uses the atomic mix approximation to the binary stochastic medium transport problem and a low-order discrete ordinates angular approximation. The second approach uses the Levermore-Pomraning model for the binary stochastic medium transport problem and a low-order discrete ordinates angular approximation. In both cases, we use Monte Carlo Algorithm B with weight windows automatically generated from the approximate forward scalar flux distribution to obtain the solution of the transport problem.
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Author: Carla Lynn Barrett
Author: Kasem Naser Abdeel
Author: Scott Allen Turner
Author: Marc. A. Cooper
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Author: Stephen A. Dupree
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