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Iterative Acceleration Methods For Monte Carlo And Deterministic Criticality Calculations
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Book Synopsis Iterative Acceleration Methods for Monte Carlo and Deterministic Criticality Calculations by :
Download or read book Iterative Acceleration Methods for Monte Carlo and Deterministic Criticality Calculations written by and published by . This book was released on 1995 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.
Book Synopsis Iterative Acceleration Methods for Monte Carlo and Deterministic Criticality Calculations by : Todd James Urbatsch
Download or read book Iterative Acceleration Methods for Monte Carlo and Deterministic Criticality Calculations written by Todd James Urbatsch and published by . This book was released on 1995 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Acceleration of Monte Carlo Criticality Calculations Using Deterministic-Based Starting Sources by :
Download or read book Acceleration of Monte Carlo Criticality Calculations Using Deterministic-Based Starting Sources written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new automatic approach that uses approximate deterministic solutions for providing the starting fission source for Monte Carlo eigenvalue calculations was evaluated in this analysis. By accelerating the Monte Carlo source convergence and decreasing the number of cycles that has to be skipped before the tallies estimation, this approach was found to increase the efficiency of the overall simulation, even with the inclusion of the extra computational time required by the deterministic calculation. This approach was also found to increase the reliability of the Monte Carlo criticality calculations of loosely coupled systems because the use of the better starting source reduces the likelihood of producing an undersampled k{sub eff} due to the inadequate source convergence. The efficiency improvement was demonstrated using two of the standard test problems devised by the OECD/NEA Expert Group on Source Convergence in Criticality-Safety Analysis to measure the source convergence in Monte Carlo criticality calculations. For a fixed uncertainty objective, this approach increased the efficiency of the overall simulation by factors between 1.2 and 3 depending on the difficulty of the source convergence in these problems. The reliability improvement was demonstrated in a modified version of the 'k{sub eff} of the world' problem that was specifically designed to demonstrate the limitations of the current Monte Carlo power iteration techniques. For this problem, the probability of obtaining a clearly undersampled k{sub eff} decreased from 5% with a uniform starting source to zero with a deterministic starting source when batch sizes with more than 15,000 neutron/cycle were used.
Book Synopsis Parallel Monte Carlo Synthetic Acceleration Methods for Discrete Transport Problems by :
Download or read book Parallel Monte Carlo Synthetic Acceleration Methods for Discrete Transport Problems written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work researches and develops Monte Carlo Synthetic Acceleration (MCSA) methods as a new class of solution techniques for discrete neutron transport and fluid flow problems. Monte Carlo Synthetic Acceleration methods use a traditional Monte Carlo process to approximate the solution to the discrete problem as a means of accelerating traditional fixed-point methods. To apply these methods to neutronics and fluid flow and determine the feasibility of these methods on modern hardware, three complementary research and development exercises are performed. First, solutions to the SPN discretization of the linear Boltzmann neutron transport equation are obtained using MCSA with a difficult criticality calculation for a light water reactor fuel assembly used as the driving problem. To enable MCSA as a solution technique a group of modern preconditioning strategies are researched. MCSA when compared to conventional Krylov methods demonstrated improved iterative performance over GMRES by converging in fewer iterations when using the same preconditioning. Second, solutions to the compressible Navier-Stokes equations were obtained by developing the Forward-Automated Newton-MCSA (FANM) method for nonlinear systems based on Newton's method. Three difficult fluid benchmark problems in both convective and driven flow regimes were used to drive the research and development of the method. For 8 out of 12 benchmark cases, it was found that FANM had better iterative performance than the Newton-Krylov method by converging the nonlinear residual in fewer linear solver iterations with the same preconditioning. Third, a new domain decomposed algorithm to parallelize MCSA aimed at leveraging leadership-class computing facilities was developed by utilizing parallel strategies from the radiation transport community. The new algorithm utilizes the Multiple-Set Overlapping-Domain strategy in an attempt to reduce parallel overhead and add a natural element of replication to the algorithm. It was found that for the current implementation of MCSA, both weak and strong scaling improved on that observed for production implementations of Krylov methods.
Book Synopsis An Automated Variance Reduction Method for Global Monte Carlo Neutral Particle Transport Problems by : Marc. A. Cooper
Download or read book An Automated Variance Reduction Method for Global Monte Carlo Neutral Particle Transport Problems written by Marc. A. Cooper and published by . This book was released on 1999 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advanced Modeling and Simulation of Nuclear Reactors by : Jingang Liang
Download or read book Advanced Modeling and Simulation of Nuclear Reactors written by Jingang Liang and published by Frontiers Media SA. This book was released on 2023-04-10 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Iterative Methods by : Louis A. Hageman
Download or read book Applied Iterative Methods written by Louis A. Hageman and published by Elsevier. This book was released on 2014-06-28 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Iterative Methods
Book Synopsis Development and Implementation of Convergence Diagnostics and Acceleration Methodologies in Monte Carlo Criticality Simulations by : Bo Shi
Download or read book Development and Implementation of Convergence Diagnostics and Acceleration Methodologies in Monte Carlo Criticality Simulations written by Bo Shi and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of the accuracy and ease of implementation, the Monte Carlo methodology is widely used in the analysis of nuclear systems. The estimated effective multiplication factor (keff) and flux distribution are statistical by their natures. In eigenvalue problems, however, neutron histories are not independent but are correlated through subsequent generations. Therefore, it is necessary to ensure that only the converged data are used for further analysis. Discarding a larger amount of initial histories would reduce the risk of contaminating the results by non-converged data, but increase the computational expense. This issue is amplified for large nuclear systems with slow convergence. One solution would be to use the convergence of keff or the flux distribution as the criterion for initiating accumulation of data. Although several approaches have been developed aimed at identifying convergence, these methods are not always reliable, especially for slow converging problems. This dissertation has attacked this difficulty by developing two independent but related methodologies. One aims to find a more reliable and robust way to assess convergence by statistically analyzing the local flux change. The other forms a basis to increase the convergence rate and thus reduce the computational expense. Eventually, these two topics will contribute to the ultimate goal of improving the reliability and efficiency of the Monte Carlo criticality calculations.
Book Synopsis Monte Carlo Methods for Applied Scientists by : Ivan Dimov
Download or read book Monte Carlo Methods for Applied Scientists written by Ivan Dimov and published by World Scientific. This book was released on 2008 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is inherently parallel and the extensive and rapid development in parallel computers, computational clusters and grids has resulted in renewed and increasing interest in this method. At the same time there has been an expansion in the application areas and the method is now widely used in many important areas of science including nuclear and semiconductor physics, statistical mechanics and heat and mass transfer. This book attempts to bridge the gap between theory and practice concentrating on modern algorithmic implementation on parallel architecture machines. Although a suitable text for final year postgraduate mathematicians and computational scientists it is principally aimed at the applied scientists: only a small amount of mathematical knowledge is assumed and theorem proving is kept to a minimum, with the main focus being on parallel algorithms development often to applied industrial problems. A selection of algorithms developed both for serial and parallel machines are provided. Sample Chapter(s). Chapter 1: Introduction (231 KB). Contents: Basic Results of Monte Carlo Integration; Optimal Monte Carlo Method for Multidimensional Integrals of Smooth Functions; Iterative Monte Carlo Methods for Linear Equations; Markov Chain Monte Carlo Methods for Eigenvalue Problems; Monte Carlo Methods for Boundary-Value Problems (BVP); Superconvergent Monte Carlo for Density Function Simulation by B-Splines; Solving Non-Linear Equations; Algorithmic Effciency for Different Computer Models; Applications for Transport Modeling in Semiconductors and Nanowires. Readership: Applied scientists and mathematicians.
Book Synopsis Fission Matrix Capability for MCNP Monte Carlo by :
Download or read book Fission Matrix Capability for MCNP Monte Carlo written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In a Monte Carlo criticality calculation, before the tallying of quantities can begin, a converged fission source (the fundamental eigenvector of the fission kernel) is required. Tallies of interest may include powers, absorption rates, leakage rates, or the multiplication factor (the fundamental eigenvalue of the fission kernel, k{sub eff}). Just as in the power iteration method of linear algebra, if the dominance ratio (the ratio of the first and zeroth eigenvalues) is high, many iterations of neutron history simulations are required to isolate the fundamental mode of the problem. Optically large systems have large dominance ratios, and systems containing poor neutron communication between regions are also slow to converge. The fission matrix method, implemented into MCNP[1], addresses these problems. When Monte Carlo random walk from a source is executed, the fission kernel is stochastically applied to the source. Random numbers are used for: distances to collision, reaction types, scattering physics, fission reactions, etc. This method is used because the fission kernel is a complex, 7-dimensional operator that is not explicitly known. Deterministic methods use approximations/discretization in energy, space, and direction to the kernel. Consequently, they are faster. Monte Carlo directly simulates the physics, which necessitates the use of random sampling. Because of this statistical noise, common convergence acceleration methods used in deterministic methods do not work. In the fission matrix method, we are using the random walk information not only to build the next-iteration fission source, but also a spatially-averaged fission kernel. Just like in deterministic methods, this involves approximation and discretization. The approximation is the tallying of the spatially-discretized fission kernel with an incorrect fission source. We address this by making the spatial mesh fine enough that this error is negligible. As a consequence of discretization we get a spatially low-order kernel, the fundamental eigenvector of which should converge faster than that of continuous kernel. We can then redistribute the fission bank to match the fundamental fission matrix eigenvector, effectively eliminating all higher modes. For all computations here biasing is not used, with the intention of comparing the unaltered, conventional Monte Carlo process with the fission matrix results. The source convergence of standard Monte Carlo criticality calculations are, to some extent, always subject to the characteristics of the problem. This method seeks to partially eliminate this problem-dependence by directly calculating the spatial coupling. The primary cost of this, which has prevented widespread use since its inception [2,3,4], is the extra storage required. To account for the coupling of all N spatial regions to every other region requires storing N2 values. For realistic problems, where a fine resolution is required for the suppression of discretization error, the storage becomes inordinate. Two factors lead to a renewed interest here: the larger memory available on modern computers and the development of a better storage scheme based on physical intuition. When the distance between source and fission events is short compared with the size of the entire system, saving memory by accounting for only local coupling introduces little extra error. We can gain other information from directly tallying the fission kernel: higher eigenmodes and eigenvalues. Conventional Monte Carlo cannot calculate this data - here we have a way to get new information for multiplying systems. In Ref. [5], higher mode eigenfunctions are analyzed for a three-region 1-dimensional problem and 2-dimensional homogenous problem. We analyze higher modes for more realistic problems. There is also the question of practical use of this information; here we examine a way of using eigenmode information to address the negative confidence interval bias due to inter-cycle correl ...
Book Synopsis A Simple Eigenfunction Convergence Acceleration Method for Monte Carlo by :
Download or read book A Simple Eigenfunction Convergence Acceleration Method for Monte Carlo written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo transport codes typically use a power iteration method to obtain the fundamental eigenfunction. The standard convergence rate for the power iteration method is the ratio of the first two eigenvalues, that is, k2/k1. Modifications to the power method have accelerated the convergence by explicitly calculating the subdominant eigenfunctions as well as the fundamental. Calculating the subdominant eigenfunctions requires using particles of negative and positive weights and appropriately canceling the negative and positive weight particles. Incorporating both negative weights and a ± weight cancellation requires a significant change to current transport codes. This paper presents an alternative convergence acceleration method that does not require modifying the transport codes to deal with the problems associated with tracking and cancelling particles of ± weights. Instead, only positive weights are used in the acceleration method.
Book Synopsis Entropy-based Diagnostics of Criticality Monte Carlo Simulation and Higher Eigenmode Acceleration Methodology by : Bo Shi
Download or read book Entropy-based Diagnostics of Criticality Monte Carlo Simulation and Higher Eigenmode Acceleration Methodology written by Bo Shi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of the accuracy and ease of implementation, Monte Carlo methodology is widely used in analysis of nuclear systems. The obtained estimate of the multiplication factor (keff) or flux distribution is statistical by its nature. In criticality simulation of a nuclear critical system, whose basis is the power iteration method, the guessed source distribution initially is generally away from the converged fundamental one. Therefore, it is necessary to ensure that the convergence is achieved before data are accumulated. Discarding a larger amount of initial histories could reduce the risk of contaminating the results by non-converged data but increases the computational expense. This issue is amplified for large loosely coupled nuclear systems with low convergence rate. Since keff is a generation-based global value, frequently no explicit criterion is applied to the diagnostic of keff directly. As an alternative, a flux-based entropy check available in MCNP5 works well in many cases. However, when applied to a difficult storage fuel pool benchmark problem, it could not always detect the non-convergence of flux distribution. Preliminary evaluation indicates that it is due to collapsing local information into a single number. This thesis addresses this problem by two new developments. First, it aims to find a more reliable way to assess convergence by analyzing the local flux change. Second, it introduces an approach to simultaneously compute both the first and second eigenmodes. At the same time, by computing these eigenmodes, this approach could increase the convergence rate. Improvement in these two areas could have a significant impact on practicality of Monte Carlo criticality simulations.
Book Synopsis Optimization of Weighted Monte Carlo Methods by : Gennadii A. Mikhailov
Download or read book Optimization of Weighted Monte Carlo Methods written by Gennadii A. Mikhailov and published by Springer. This book was released on 1992-02-13 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is based on the munerical realization of natural or artificial models of the phenomena under considerations. In contrast to classical computing methods the Monte Carlo efficiency depends weakly on the dimen sion and geometric details of the problem. The method is used for solving complex problems of the radiation transfer theory, turbulent diffusion, chemi cal kinetics, theory of rarefied gases, diffraction of waves on random surfaces, etc. The Monte Carlo method is especially effective when using multi-processor computing systems which allow many independent statistical experiments to be simulated simultaneously. The weighted Monte Carlo estimates are constructed in order to diminish errors and to obtain dependent estimates for the calculated functionals for different values of parameters of the problem, i.e., to improve the functional dependence. In addition, the weighted estimates make it possible to evaluate special functionals, for example, the derivatives with respect to the parameters. There are many works concerned with the development of the weighted estimates. In Chap. 1 we give the necessary information about these works and present a set of illustrations. The rest of the book is devoted to the solution of a series of mathematical problems related to the optimization of the weighted Monte Carlo estimates.
Book Synopsis Monte Carlo Methods by : Malvin H. Kalos
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by Wiley-VCH. This book was released on 2009-06-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Book Synopsis Transactions of the American Nuclear Society by : American Nuclear Society
Download or read book Transactions of the American Nuclear Society written by American Nuclear Society and published by . This book was released on 2001 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book INIS Atomindex written by and published by . This book was released on 1996 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Government Reports Announcements & Index by :
Download or read book Government Reports Announcements & Index written by and published by . This book was released on 1996 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:
