Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Iterative methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Evaluation of gamma-ray transmission through rectangular collimator slits for application in nuclear fuel spectrometry

Gamma-ray spectrometry is widely applied in several science fields, and in particular in non-destructive gamma scanning and gamma emission tomography of irradiated nuclear fuel. Usually, a collimator is used in the experimental setup, to selectively interrogate a region of interest in the fuel. For the optimization of instrument design, as well as for planning measurement campaigns, predictive models for the transmitted gamma-ray intensity through the collimator are needed. Commonly, Monte Carlo Radiation Transport tools are used for accurate prediction of gamma-ray transport, however, the long computation time requirements when used in low-efficiency experimental setups present challenges. Here, the full-energy peak intensity transmitted through a rectangular collimator slit was examined. A uniform planar surface source emitting isotropically was considered, and the rate of photons reaching an ideal counter plane on the opposite side of the collimator was evaluated by analytical integration. To find a closed-form primitive function, some idealizations were required, and thereby parametric models were obtained for the optical field of view, dependent on slit dimensions (length, height and width) and source-to-collimator distance. For contributions from outside the optical field of view, where a closed-form expression cannot be found, fast numerical integral methods were instead used. The results were validated using the Monte Carlo code MCNP6 and show an agreement within three percent for the numerical method. For the analytical method, deviations up to tens of percent were obtained, which is deemed to still be sufficient for instrument design and measurement planning, where often the order of magnitude of the count rate is not a priori known. The method is planned for use in iterative optimization routines in the design of Gamma Emission Tomography devices, as well as for the prediction of gamma spectra obtained in the planning of fuel inspections. An application of the proposed method was demonstrated in spectrum prediction for a short cooling-time fuel rod test from the Halden reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the equivalent Dancoff factor cell method performing slowing down calculations on the fly for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for pin-cell, unit-cell, and fuel assembly problems with various resonance self-shielding conditions based on very high temperature reactor, high temperature test reactor, and Empire benchmark cores, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also showed that the methodology worked well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Bayesian Model Averaging for Ensemble-Based Estimates of Solvation Free Energies

This paper applies the Bayesian Model Averaging (BMA) statistical ensemble technique to estimate small molecule solvation free energies. There is a wide range methods for predicting solvation free energies, ranging from empirical statistical models to {\it ab initio} quantum mechanical approaches. Each of these methods are based on a set of conceptual assumptions that can affect a method's predictive accuracy and transferability. Using an iterative statistical process, we have selected and combined solvation energy estimates using an ensemble of 17 diverse methods from the SAMPL4 blind prediction study to form a single, aggregated solvation energy estimate. The ensemble design process evaluates the statistical information in each individual method as well as the performance of the aggregate estimate obtained from the ensemble as a whole. Methods that possess minimal or redundant information are pruned from the ensemble and the evaluation process repeats until aggregate predictive performance can no longer be improved. We show that this process results in a final aggregate estimate that outperforms all individual methods by reducing estimate errors by as much as 91% to 1.2 kcal/mol accuracy. We also compare our iterative refinement approach to other statistical ensemble approaches and demonstrate that this iterative process reduces estimate errors by as much as 61%. This work provides a new approach for accurate solvation free energy prediction and lays the foundation for future work on aggregate models that can balance computational cost with predictive accuracy.

solvation, Bayesian model averaging, Electrostatic↗
DOE OSTI2016

SU-C-209-02: 3D Fluoroscopic Image Generation From Patient-Specific 4DCBCT-Based Motion Models Derived From Clinical Patient Images

Purpose: We develop a method to generate time varying volumetric images (3D fluoroscopic images) using patient-specific motion models derived from four-dimensional cone-beam CT (4DCBCT). Methods: Motion models are derived by selecting one 4DCBCT phase as a reference image, and registering the remaining images to it. Principal component analysis (PCA) is performed on the resultant displacement vector fields (DVFs) to create a reduced set of PCA eigenvectors that capture the majority of respiratory motion. 3D fluoroscopic images are generated by optimizing the weights of the PCA eigenvectors iteratively through comparison of measured cone-beam projections and simulated projections generated from the motion model. This method was applied to images from five lung-cancer patients. The spatial accuracy of this method is evaluated by comparing landmark positions in the 3D fluoroscopic images to manually defined ground truth positions in the patient cone-beam projections. Results: 4DCBCT motion models were shown to accurately generate 3D fluoroscopic images when the patient cone-beam projections contained clearly visible structures moving with respiration (e.g., the diaphragm). When no moving anatomical structure was clearly visible in the projections, the 3D fluoroscopic images generated did not capture breathing deformations, and reverted to the reference image. For the subset of 3D fluoroscopic images generated from projections with visibly moving anatomy, the average tumor localization error and the 95th percentile were 1.6 mm and 3.1 mm respectively. Conclusion: This study showed that 4DCBCT-based 3D fluoroscopic images can accurately capture respiratory deformations in a patient dataset, so long as the cone-beam projections used contain visible structures that move with respiration. For clinical implementation of 3D fluoroscopic imaging for treatment verification, an imaging field of view (FOV) that contains visible structures moving with respiration should be selected. If no other appropriate structures are visible, the images should include the diaphragm. This project was supported, in part, through a Master Research Agreement with Varian Medical Systems, Inc, Palo Alto, CA.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

The Lattice Boltzmann Method applied to neutron transport

In this paper the applicability of the Lattice Boltzmann Method to neutron transport is investigated. One of the main features of the Lattice Boltzmann method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. An iterative solution of the operator form of the neutron transport equation is presented here, with the first collision source as the starting point of the iteration scheme. A full description of the discretization scheme is given, along with the quadrature set used for the angular discretization. An angular refinement scheme is introduced to increase the angular coverage of the problem phase space and to mitigate lattice ray effects. The method is applied to a model problem to investigate its applicability to neutron transport and the results are compared to a reference solution calculated, using MCNP. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Numerical algorithms for water waves with background flow over obstacles and topography

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Ambrose, David M.↗
DOE OSTI2011

Reduction of density-modification bias by β correction

A cross-validation-based method for bias reduction in ‘classical’ iterative density modification of experimental X-ray crystallography maps provides significantly more accurate phase-quality estimates and leads to improved automated model building. Density modification often suffers from an overestimation of phase quality, as seen by escalated figures of merit. A new cross-validation-based method to address this estimation bias by applying a bias-correction parameter ‘β’ to maximum-likelihood phase-combination functions is proposed. In tests on over 100 single-wavelength anomalous diffraction data sets, the method is shown to produce much more reliable figures of merit and improved electron-density maps. Furthermore, significantly better results are obtained in automated model building iterated with phased refinement using the more accurate phase probability parameters from density modification.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

An efficient polyenergetic SART (pSART) reconstruction algorithm for quantitative myocardial CT perfusion

Purpose: In quantitative myocardial CT perfusion imaging, beam hardening effect due to dense bone and high concentration iodinated contrast agent can result in visible artifacts and inaccurate CT numbers. In this paper, an efficient polyenergetic Simultaneous Algebraic Reconstruction Technique (pSART) was presented to eliminate the beam hardening artifacts and to improve the CT quantitative imaging ability. Methods: Our algorithm made threea priori assumptions: (1) the human body is composed of several base materials (e.g., fat, breast, soft tissue, bone, and iodine); (2) images can be coarsely segmented to two types of regions, i.e., nonbone regions and noniodine regions; and (3) each voxel can be decomposed into a mixture of two most suitable base materials according to its attenuation value and its corresponding region type information. Based on the above assumptions, energy-independent accumulated effective lengths of all base materials can be fast computed in the forward ray-tracing process and be used repeatedly to obtain accurate polyenergetic projections, with which a SART-based equation can correctly update each voxel in the backward projecting process to iteratively reconstruct artifact-free images. This approach effectively reduces the influence of polyenergetic x-ray sources and it further enables monoenergetic images to be reconstructed at any arbitrarily preselected target energies. A series of simulation tests were performed on a size-variable cylindrical phantom and a realistic anthropomorphic thorax phantom. In addition, a phantom experiment was also performed on a clinical CT scanner to further quantitatively validate the proposed algorithm. Results: The simulations with the cylindrical phantom and the anthropomorphic thorax phantom showed that the proposed algorithm completely eliminated beam hardening artifacts and enabled quantitative imaging across different materials, phantom sizes, and spectra, as the absolute relative errors were reduced from [−7.5%, 12.1%] for SART to [−0.1%, 0.1%] for pSART. When using low kVp spectra and high reference energies, pSART also showed improved reconstruction efficiency in terms of convergence speed compared to the conventional SART algorithm. The phantom experiment on a clinical CT scanner indicated that the quantitative advantage of pSART is realizable in experimental CT acquisition, as the absolute relative errors across material inserts were less than 0.4%. Conclusions: By incorporatinga priori information (material attenuation coefficients, x-ray source spectrum, and region type information) into the reconstruction process, the proposed pSART algorithm could effectively eliminate beam hardening artifacts, reconstruct the accurate attenuation coefficients for precise quantitative imaging, and accelerate the reconstruction process.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

WE-EF-207-09: Single-Scan Dual-Energy CT Using Primary Modulation

Purpose: Compared with conventional CT, dual energy CT (DECT) provides better material differentiation but requires projection data with two different effective x-ray spectra. Current DECT scanners use either a two-scan setting or costly imaging components, which are not feasible or available on open-gantry cone-beam CT systems. We propose a hardware-based method which utilizes primary modulation to enable single-scan DECT on a conventional CT scanner. The CT imaging geometry of primary modulation is identical to that used in our previous method for scatter removal, making it possible for future combination with effective scatter correction on the same CT scanner. Methods: We insert an attenuation sheet with a spatially-varying pattern - primary modulator-between the x-ray source and the imaged object. During the CT scan, the modulator selectively hardens the x-ray beam at specific detector locations. Thus, the proposed method simultaneously acquires high and low energy data. High and low energy CT images are then reconstructed from projections with missing data via an iterative CT reconstruction algorithm with gradient weighting. Proof-of-concept studies are performed using a copper modulator on a cone-beam CT system. Results: Our preliminary results on the Catphan(c) 600 phantom indicate that the proposed method for single-scan DECT is able to successfully generate high-quality high and low energy CT images and distinguish different materials through basis material decomposition. By applying correction algorithms and using all of the acquired projection data, we can reconstruct a single CT image of comparable image quality to conventional CT images, i.e., without primary modulation. Conclusion: This work shows great promise in using a primary modulator to perform high-quality single-scan DECT imaging. Future studies will test method performance on anthropomorphic phantoms and perform quantitative analyses on image qualities and DECT decomposition accuracy. We will use simulations to optimize the modulator material and geometry parameters.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

Incorporating a completely renormalized coupled cluster approach into a composite method for thermodynamic properties and reaction paths

The correlation consistent composite approach (ccCA), using the S4 complete basis set two-point extrapolation scheme (ccCA-S4), has been modified to incorporate the left-eigenstate completely renormalized coupled cluster method, including singles, doubles, and non-iterative triples (CR-CC(2,3)) as the highest level component. The new ccCA-CC(2,3) method predicts thermodynamic properties with an accuracy that is similar to that of the original ccCA-S4 method. At the same time, the inclusion of the single-reference CR-CC(2,3) approach provides a ccCA scheme that can correctly treat reaction pathways that contain certain classes of multi-reference species such as diradicals, which would normally need to be treated by more computationally demanding multi-reference methods. The new ccCA-CC(2,3) method produces a mean absolute deviation of 1.7 kcal/mol for predicted heats of formation at 298 K, based on calibration with the G2/97 set of 148 molecules, which is comparable to that of 1.0 kcal/mol obtained using the ccCA-S4 method, while significantly improving the performance of the ccCA-S4 approach in calculations involving more demanding radical and diradical species. Both the ccCA-CC(2,3) and ccCA-S4 composite methods are used to characterize the conrotatory and disrotatory isomerization pathways of bicyclo[1.1.0]butane to trans-1,3-butadiene, for which conventional coupled cluster methods, such as the CCSD(T) approach used in the ccCA-S4 model and, in consequence, the ccCA-S4 method itself might fail by incorrectly placing the disrotatory pathway below the conrotatory one. The ccCA-CC(2,3) scheme provides correct pathway ordering while providing an accurate description of the activation and reaction energies characterizing the lowest-energy conrotatory pathway. The ccCA-CC(2,3) method is thus a viable method for the analyses of reaction mechanisms that have significant multi-reference character, and presents a generally less computationally intensive alternative to true multi-reference methods, with computer costs and ease of use that are similar to those that characterize the more established, CCSD(T)-based, ccCA-S4 methodology.

36 MATERIALS SCIENCE↗
DOE OSTI2016

SU-F-J-111: A Novel Distance-Dose Weighting Method for Label Fusion in Multi- Atlas Segmentation for Prostate Radiation Therapy

Purpose: A novel distance-dose weighting method for label fusion was developed to increase segmentation accuracy in dosimetrically important regions for prostate radiation therapy. Methods: Label fusion as implemented in the original SIMPLE (OS) for multi-atlas segmentation relies iteratively on the majority vote to generate an estimated ground truth and DICE similarity measure to screen candidates. The proposed distance-dose weighting puts more values on dosimetrically important regions when calculating similarity measure. Specifically, we introduced distance-to-dose error (DDE), which converts distance to dosimetric importance, in performance evaluation. The DDE calculates an estimated DE error derived from surface distance differences between the candidate and estimated ground truth label by multiplying a regression coefficient. To determine the coefficient at each simulation point on the rectum, we fitted DE error with respect to simulated voxel shift. The DEs were calculated by the multi-OAR geometry-dosimetry training model previously developed in our research group. Results: For both the OS and the distance-dose weighted SIMPLE (WS) results, the evaluation metrics for twenty patients were calculated using the ground truth segmentation. The mean difference of DICE, Hausdorff distance, and mean absolute distance (MAD) between OS and WS have shown 0, 0.10, and 0.11, respectively. In partial MAD of WS which calculates MAD within a certain PTV expansion voxel distance, the lower MADs were observed at the closer distances from 1 to 8 than those of OS. The DE results showed that the segmentation from WS produced more accurate results than OS. The mean DE error of V75, V70, V65, and V60 were decreased by 1.16%, 1.17%, 1.14%, and 1.12%, respectively. Conclusion: We have demonstrated that the method can increase the segmentation accuracy in rectum regions adjacent to PTV. As a result, segmentation using WS have shown improved dosimetric accuracy than OS. The WS will provide dosimetrically important label selection strategy in multi-atlas segmentation. CPRIT grant RP150485.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Radiative recombination data for tungsten ions: III. W{sup 14+}–W{sup 23+}

This paper completes the cycle of our calculations of the radiative recombination and photoionization data for tungsten ions. Presented here are the photoionization and radiative recombination cross sections, radiative recombination rate coefficients, and radiated power loss rate coefficients for ten tungsten impurity ions from W{sup 14+} to W{sup 23+}. These data are required in diagnostics and modeling fusion plasmas studied in such devices as ITER, ASDEX Upgrade, and EBIT. Partial photoionization cross sections have been fitted by an analytical expression with five fit parameters tabulated here. Total radiative recombination cross sections are presented in the electron energy range from 1 eV to ∼80 keV. Radiative recombination rates and radiated power loss rates are given in the temperature range from 10{sup 4} K to 10{sup 9} K. Calculations have been performed on the basis of the fully relativistic treatment of photoionization and radiative recombination taking into account all significant multipoles of the radiative field. Electron wave functions have been obtained by the Dirac–Fock method with the proper consideration of the electron exchange. The relativistic Maxwell–Jüttner distribution of continuum electrons has been used in calculations of radiative recombination rates and radiated power loss rates. This decreases values of the rates noticeably at a high temperature as compared to the usual non-relativistic Maxwell–Boltzmann distribution. -- Highlights: •Radiative recombination data for ten tungsten ions W{sup 14+}–W{sup 23+} are presented. •Photoionization cross sections are also given. •Calculations are fully relativistic including all multipoles of the radiative field. •We use the Dirac–Fock method to obtain the electron wave functions. •The data are required for diagnostics and modeling fusion plasmas studied in ITER.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Multi-stage preconditioners for thermal–compositional–reactive flow in porous media

We present a family of multi-stage preconditioners for coupled thermal-compositional-reactive reservoir simulation problems. The most common preconditioner used in industrial practice, the Constrained Pressure Residual (CPR) method, was designed for isothermal models and does not offer a specific strategy for the energy equation. For thermal simulations, inadequate treatment of the temperature unknown can cause severe conver-gence degradation. When strong thermal diffusion is present, the energy equation exhibits significant elliptic behavior that cannot be accurately corrected by CPR's second stage. In this work, we use Schur-complement decompositions to extract a temperature subsystem and apply an Algebraic MultiGrid (AMG) approximation as an additional preconditioning stage to improve the treatment of the energy equation. We present results for several two-dimensional hot air injection problems using an extra heavy oil, including challenging reactive In-Situ Combustion (ISC) cases. We show improved performance and robustness across different thermal regimes, from advection dominated (high Péclet number) to diffusion dominated (low Péclet number). The number of linear iterations is reduced by 40–85% compared to standard CPR for both homogeneous and heterogeneous media, and the new methods exhibit almost no sensitivity to the thermal regime.

42 ENGINEERING↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A Multiple-Set Overlapping-Domain Decomposed Monte Carlo Synthetic Acceleration Method for Linear Systems

We present a multiple-set overlapping-domain decomposed strategy for parallelizing the Monte Carlo Synthetic Acceleration method. Monte Carlo Synthetic Acceleration methods use the Neumann-Ulam class of Monte Carlo solvers for linear systems to accelerate a fixed-point iteration sequence. Effective parallel algorithms for these methods require the parallelization of the underlying Neumann-Ulam solvers. To do this in a domain decomposed environment, we borrow strategies traditionally implemented in Monte Carlo particle transport to parallelize the problem. The parallel Neumann-Ulam and multiple-set overlapping-domain decomposition algorithms are presented along with parallel scaling data for the resulting implementation using the Titan Cray XK7 machine at Oak Ridge National Laboratory.

Computer Science↗
DOE OSTI2014

Discontinuous diffusion synthetic acceleration for S{sub n} transport on 2D arbitrary polygonal meshes

In this paper, a Diffusion Synthetic Acceleration (DSA) technique applied to the S{sub n} radiation transport equation is developed using Piece-Wise Linear Discontinuous (PWLD) finite elements on arbitrary polygonal grids. The discretization of the DSA equations employs an Interior Penalty technique, as is classically done for the stabilization of the diffusion equation using discontinuous finite element approximations. The penalty method yields a system of linear equations that is Symmetric Positive Definite (SPD). Thus, solution techniques such as Preconditioned Conjugate Gradient (PCG) can be effectively employed. Algebraic MultiGrid (AMG) and Symmetric Gauss–Seidel (SGS) are employed as conjugate gradient preconditioners for the DSA system. AMG is shown to be significantly more efficient than SGS. Fourier analyses are carried out and we show that this discontinuous finite element DSA scheme is always stable and effective at reducing the spectral radius for iterative transport solves, even for grids with high-aspect ratio cells. Numerical results are presented for different grid types: quadrilateral, hexagonal, and polygonal grids as well as grids with local mesh adaptivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗