Download or read book The Solution of Radiation Transport Equations with Adaptive Finite Elements Final Report Nasa written by United States. National Aeronautics and Space Administration and published by . This book was released on 2002* with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Solution of Radiation Transport Equations with Adaptive Finite Elements written by Linda Stals and published by . This book was released on 2001 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We compare the performance of an inexact Newton-multigrid method and Full Approximation Storage multigrid when solving radiation transport equations. We also present an adaptive refinement algorithm and explore its impact on the solution of such equations."

Download or read book Finite Element Methods for Particle Transport written by Ron Tunstall Ackroyd and published by Taylor & Francis Group. This book was released on 1997 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the transport of neutral particles, neutrons and photons, using the finite element method to address practical problems in nuclear power and mineral prospecting. Includes discussions of how the method began and has matured to become a practical tool complementing the stochastic Monte Carlo method, spatial finite elements, examples of calculations, equivalent forms of the Boltzmann equation, neutron streaming in voids, some aspects of discontinuous variational solutions, complementary principles and benchmarking, time-dependent transport, and modelling three-dimensional systems. Double spaced. Annotation copyright by Book News, Inc., Portland, OR

Download or read book Coupled Space angle Adaptivity and Goal oriented Error Control for Radiation Transport Calculations written by HyeongKae Park and published by . This book was released on 2006 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this thesis is to develop a posteriori error analysis in a coupled space-angle framework and an efficient adaptive algorithm. Moreover, the mesh refinement strategy which is tuned for minimizing the error in the target engineering output has been developed by employing the dual argument of the problem. This numerical framework has been implemented in the general-purpose neutral particle code EVENT for assessment.

Download or read book Application of New Variational Principles in Finite Element Method Solutions of the Radiation Transport Equation written by Mehran Pourzand and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Higher Order Discontinuous Finite Element Methods for Discrete Ordinates Thermal Radiative Transfer written by Peter Gregory Maginot and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear discontinuous finite element method (LDFEM) is the current work horse of the radiation transport community. The popularity of LDFEM is a result of LDFEM (and its Q1 multi-dimensional extensions) being both accurate and preserving the thick diffusion limit. In practice, the LDFEM equations must be "lumped" to mitigate negative radiation transport solutions. Negative solutions are non-physical, but are inherent to the mathematics of LDFEM and other spatial discretizations. Ongoing changes in high performance computing (HPC) are dictating a preference for increased numbers of floating point operations (FLOPS) per unknown. Higher order discontinuous finite element methods (DFEM), those with polynomial trial spaces greater than linear, have been found to offer more accuracy per unknown than LDFEM. However, DFEM with higher degree trial spaces have received only limited attention due to their increased computational time per unknown, LDFEM's preservation of the thick diffusion limit, and the relative accuracy of LDFEM compared to other historical spatial discretizations. As solution methods evolve to make the most efficient use of HPC, it is possible that the increased computational work of higher order DFEM may become a strength rather than a hindrance. For higher order DFEM to be useful in practice, lumping techniques must be developed to inhibit negative radiation transport solutions. We will show that traditional mass matrix lumping does not guarantee positive solutions and limits the overall accuracy of the DFEM scheme. To solve this problem, we propose a new, quadrature based, self-lumping technique. Our self-lumping technique does not limit solution order of convergence, improves solution positivity, and can be easily adapted to account for the within cell variation of interaction cross section. To test and demonstrate the characteristics of our self-lumping methodology, we apply our schemes to several test problems: a homogeneous, source-free pure absorber; a pure absorber with spatially varying cross section; a model fuel depletion problem; and finally, we solve the grey thermal radiative transfer equations. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155489

Download or read book Adaptive Finite Elements for Nonlinear Transport Equations written by Brian Ross Carnes and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Application of New Variational Principles for Finite Element Solutions of the Radiation Transport Equation written by and published by . This book was released on 1994 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Performance Analysis of the Finite Element spherical Harmonics Radiation Transport Method written by Aliva Pattnaik and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the parallel performance of the finite element-spherical harmonics (FE-PN) method implemented in the general-purpose radiation transport code EVENT is studied both analytically and empirically. EVENT solves the coupled set of space-angle discretized FE-PN equations using a parallel block-Jacobi domain decomposition method. As part of the analytical study, the thesis presents complexity results for EVENT when solving for a 3D criticality benchmark radiation transport problem in parallel. The empirical analysis is concerned with the impact of the main algorithmic factors affecting performance. Firstly, EVENT supports two solution strategies, namely MOD (Moments Over Domains) and DOM (Domains Over Moments), to solve the transport equation in parallel. The two strategies differ in the way they solve the multi-level space-angle coupled systems of equations. The thesis presents empirical evidence of which of the two solution strategies is more efficient. Secondly, different preconditioners are used in the Preconditioned Conjugate Gradient (PCG) inside EVENT. Performance of EVENT is compared when using three preconditioners, namely diagonal, SSOR(Symmetric Successive Over-Relaxation) and ILU. The other two factors, angular and spatial resolutions of the problem affect both the performance and precision of EVENT. The thesis presents comparative results on EVENTs performance as these two resolutions are increased. From the empirical performance study of EVENT, a bottleneck is identified that limits the improvement in performance as number of processors used by EVENT is increased. In some experiments, it is observed that uneven assignment of computational load among processors causes a significant portion of the total time being spent in synchronization among processors. The thesis presents two indicators that identify when such inefficiency occur; and in such a case, a load rebalancing strategy is applied that computes a new partition of the problem so that each partition corresponds to equal amount of computational load.

Download or read book An adaptive discontinuous finite element method for the transport equation written by Jens Lang and published by . This book was released on 1991 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Finite Element Solution of the Transport Equation written by Frederick A. Tarantino (CAPT, USA.) and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Solution of Partial Differential Equations written by Petter Bjorstad and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad of the Institutt for Informatikk, University of Bergen and Mitchell Luskin of the School of Mathematics, University of Minnesota for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computers offer the promise of greatly increased perfor mance and the routine calculation of previously intractable problems. The papers in this volume were presented at the IMA workshop on the Paral lel Solution of PDE held during June 9-13, 1997. The workshop brought together leading numerical analysts, computer scientists, and engineers to assess the state-of-the-art and to consider future directions.

Download or read book ICASE Semiannual Report written by and published by . This book was released on 2002 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report summarizes research conducted at ICASE in applied mathematics, computer science, fluid mechanics, and structures and material sciences during the period October 1, 2000 through March 31, 2001.

Download or read book A Finite Element Solution of the Transport Equation written by F. A. Tarantino and published by . This book was released on 1985 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a self adjoint form of the transport equation expressed as a variational integral, finite element equations for the one dimensional, one speed, homogeneous, time independent transport equation in slab geometry were derived and envoded in Fortran 77. The accuracy of C sub 0 and C sub 1 continuous fits was compared against an analytical solution for the case of noscatter. It was found that the C fits require an excessive amount of mesh refinement. The C sub 1 fit is very accurate, and does not appear to be computationally excessive. The finite element results were then compared, for the case of isotropic scatter, to a legendre polynomial solution, and the results of a recently developed code known as Ln. The methods accuracy was sufficiently verified with inexact scattering term evaluation. A technique of exact scattering integral evaluation is proposed that should reduce the amount of refinement required for convergence, and improve computational efficiency. Additional keywords: theses; numerical analysis; interpolation; computer programs. (Author).

Download or read book Finite Element Radiation Transport in One Dimension written by and published by . This book was released on 1997 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature 'in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte's two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases.

Download or read book Solution of the transport equation by variational finite element approximations written by Juhani Pitkaeranta and published by . This book was released on 1975 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solution of the Transport Equation by Variational Finite element Approximations written by Juhani Pitkäranta and published by . This book was released on 1975 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: