Figure 5 - uploaded by Jim E. Morel
Content may be subject to copyright.
Source publication
Abstract Discontinuous finite element methods,for the S equations on 3-D unstruc- tured tetrahedral and hexahedral meshes,are presented. Solution techniques in- cluding source iteration and diffusion-synthetic acceleration are described. Nu- merical results are presented which demonstrate,the accuracy and efficiency of these methods. 2
Similar publications
In this study, the Galerkin finite element method is applied to get the numerical solution of the linear telegraph equation by using cubic B‐spline function. Differently from the existing studies, the fourth order one‐step method is used to discretize in time the telegraph equation. The efficiency and accuracy of the proposed method is studied by t...
In this paper, a new $P_{2}-P_{1}$ finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn's inequality hold on general triangulations. It yields exactly divergence-free velocity approximations when applied to models of incompressible flows. The robust capacity of the pair for in...
In this paper, the effect of the Lumped Mass Matrices (LMM) on the dynamic response of beams under uniformly distributed moving loads is investigated. The analysis was done by using finite element method. In this study, material properties, throughout the length of the beams under consideration are assumed to be homogeneous. The elements stiffness,...
In this paper a general superconvergence of nonconforming finite element method for the second order elliptic problem is derived. In order to verify and support the theoretical results numerical examples are given.
In this work, we consider a multi-dimensional dual-phase-lag problem arising in porous-thermoelasticity with microtemperatures. An existence and uniqueness result is proved by applying the semigroup of linear operators theory. Then, by using the finite element method and the Euler scheme, a fully discrete approximation is numerically studied, provi...
Citations
In 1968, Bengt Carlson and Kaye Lathrop published a comprehensive review on the state of the art in discrete-ordinates (SN) calculations [10]. At that time, SN methodology existed primarily for reactor physics simulations. By today’s standards, those capabilities were limited, due
to the less-developed theoretical state of SN methods and the slower and smaller computers that were then available. In this chapter, we review some of the major advances
in SN methodology that have occurred since 1968. These advances, combined with the faster speeds and larger memories of today’s
computers, enable today’s SN codes to simulate problems of much greater complexity, realism, and physical variety. Since 1968, several books and reviews
on general numerical methods for SN simulations have been published [32, 46, 71], but none of these covers the advanced work done during the past 20 years.
The UNIC code is being developed as part of the DOE's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. UNIC is an unstructured, deterministic neutron transport code that allows a highly detailed description of a nuclear reactor co re in our numerical simulations. The goal of our simulation efforts is to reduce the uncertainties a nd biases in reactor design calculations by progres sively replacing existing multi-level averaging (homogeniz ation) techniques with more direct solution methods based on first principles. Since the neutron transp ort equation is seven dimensional (three in space, two in angle, one in energy, and one in time), these simul ations are among the most memory and computationally intensive in all of computational science. To model the complex geometry of a reactor core, billions o f spatial elements, hundreds of angles, and thousands of energy groups are necessary, which leads to pro blem sizes with petascale degrees of freedom. Therefore, these calculations exhaust memory resources on cur rent and even next-generation architectures. In this pap er, we present UNIC simulation results for two impo rtant representative problems in reactor design/analysis - PHENIX and ZPR. In each case, UNIC shows excellent weak scalability on up to 163,840 cores of BlueGene /P (Argonne) and 131,072 cores of XT5 (ORNL). While our current per processor performance is not ideal, we demonstrate a clear ability to effectivel y utilize the leadership computing platforms. Over th e coming months, we aim to improve the per-processor performance while maintaining the high parallel eff iciency by employing better algorithms (such as spa tial p-refinement, optimized matrix-tensor operations, a nd weighted partitioning for load balancing). Combi ning these additional algorithmic improvements with larg er parallel machines in the near future should allo w us to realize our long term goal of explicit geometry coupled multiphysics reactor simulations. In the lo ng run, these high fidelity simulations will be able to rep lace expensive mockup experiments and reduce the uncertainty in crucial reactor design and operation al parameters.
The aim of this work is to validate a deterministic radiation transport based treatment planning system (TPS) for single 192Ir brachytherapy source dosimetry in homogeneous water geometries.
TPS results were obtained using the deterministic radiation transport option of a BRACHYVISION v. 8.8 system for three characteristic source designs (VS2000, GMPlus HDR, and GMPlus PDR) with each source either centered in a 15 cm radius spherical water phantom, or positioned at varying distance away from the phantom center. Corresponding MC simulations were performed using the MCNPX code v.2.5.0 and source geometry models prepared using information provided by the manufacturers.
Comparison in terms of the AAPM TG-43 dosimetric formalism quantities, as well as dose rate distributions per unit air kerma strength with a spatial resolution of 0.1 cm, yielded close agreement between TPS and MC results for the sources centered in the phantom. Besides some regions close to the source longitudinal axes where discrepancies could be characterized as systematic, overall agreement for all three sources studied is comparable to the statistical (type A) uncertainty of MC simulations (1% at the majority of points in the geometry increasing to 2%-3% at points lying both away from the source center and close to the source longitudinal axis). A corresponding good agreement was also found between TPS and MC results for the sources positioned away from the phantom center.
Results of this work attest the capability of the TPS to accurately account for the scatter conditions regardless of the size or shape of a given geometry of dosimetric interest, and the position of a source within it. This is important since, as shown in the literature and summarized also in this work, these factors could introduce a significant dosimetric effect that is currently ignored in clinical treatment planning. It is concluded that the implementation of the deterministic radiation transport option of the BRACHYVISION v. 8.8 system for 192Ir brachytherapy dosimetry in homogeneous water geometries yields results of comparable accuracy to the golden standard of Monte Carlo simulation, in clinically viable calculation times.
