Goalbased angular adaptivity applied to a waveletbased discretisation of the neutral particle transport equation
Abstract
A method for applying goalbased adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an innerelement subgrid scale finite element method. The goalbased adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goalbased error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goalbased adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation.  Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvementsmore »
 Authors:
 Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ (United Kingdom)
 ANSWERS Software Service, AMEC, Kimmeridge House, Dorset Green Technology Park, Winfrith Newburgh, Dorchester, Dorset, DT2 8ZB (United Kingdom)
 AWE, Aldermaston, Reading, RG7 4PR (United Kingdom)
 Publication Date:
 OSTI Identifier:
 22382176
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; DIFFERENTIAL EQUATIONS; ERRORS; FINITE ELEMENT METHOD; NEUTRALPARTICLE TRANSPORT; RESOLUTION; SPHERICAL CONFIGURATION; TRANSPORT THEORY
Citation Formats
Goffin, Mark A., Email: mark.a.goffin@gmail.com, Buchan, Andrew G., Dargaville, Steven, Pain, Christopher C., Smith, Paul N., and SmedleyStevenson, Richard P. Goalbased angular adaptivity applied to a waveletbased discretisation of the neutral particle transport equation. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.10.063.
Goffin, Mark A., Email: mark.a.goffin@gmail.com, Buchan, Andrew G., Dargaville, Steven, Pain, Christopher C., Smith, Paul N., & SmedleyStevenson, Richard P. Goalbased angular adaptivity applied to a waveletbased discretisation of the neutral particle transport equation. United States. doi:10.1016/J.JCP.2014.10.063.
Goffin, Mark A., Email: mark.a.goffin@gmail.com, Buchan, Andrew G., Dargaville, Steven, Pain, Christopher C., Smith, Paul N., and SmedleyStevenson, Richard P. 2015.
"Goalbased angular adaptivity applied to a waveletbased discretisation of the neutral particle transport equation". United States.
doi:10.1016/J.JCP.2014.10.063.
@article{osti_22382176,
title = {Goalbased angular adaptivity applied to a waveletbased discretisation of the neutral particle transport equation},
author = {Goffin, Mark A., Email: mark.a.goffin@gmail.com and Buchan, Andrew G. and Dargaville, Steven and Pain, Christopher C. and Smith, Paul N. and SmedleyStevenson, Richard P.},
abstractNote = {A method for applying goalbased adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an innerelement subgrid scale finite element method. The goalbased adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goalbased error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goalbased adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation.  Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.},
doi = {10.1016/J.JCP.2014.10.063},
journal = {Journal of Computational Physics},
number = ,
volume = 281,
place = {United States},
year = 2015,
month = 1
}

This article presents a method for goalbased anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of eachmore »

Waveletbased neural network with fuzzylogic adaptivity for nuclear image restoration
A novel waveletbased neural network with fuzzylogic adaptivity (WNNFA) is proposed for image restoration using a nuclear medicine gamma camera based on the measured system point spread function. The objective is to restore image degradation due to photon scattering and collimator photon penetration with the gamma camera and allow improved quantitative external measurements of radionuclides in vivo. The specific clinical model proposed is the imaging of bremsstrahlung radiation using {sup 32}P and {sup 90}Y because of the enhanced image degradation effects of photon scattering, photon penetration and poor signaltonoise ratio (SNR) in measurements of this type with the gamma camera.more » 
Stochastic perturbation analysis applied to neutral particle transport
In the development of stochastic simulation methods applied to radiation transport problems sensitivity analysis and perturbation calculus has so far been a neglected area. In proportion to the rich literature on the theory of stochastic simulations and the countless papers describing its application to a specific class of problems, the aspect of Monte Carlo perturbation algorithms has been dealt with only sporadically in the context of specific problems. Until quite recently most Monte Carlo programs had to be run on expensive mainframe computers. The advent of inexpensive systems based on mass produced CPUs, as for example powerful workstations, Transputers ormore » 
Standard and goaloriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes
Standard and goaloriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angularmoment information rather than on directional information, leading to directionindependent adapted meshes. An error estimate based on a twomesh approach and a jumpbased error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goaloriented AMR procedure is devised and aims at reducing the error in userspecified quantities of interest. The quantities of interest aremore » 
Standard and goaloriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes
Standard and goaloriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angularmoment information rather than on directional information, leading to directionindependent adapted meshes. An error estimate based on a twomesh approach and a jumpbased error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goaloriented AMR procedure is devised and aims at reducing the error in userspecified quantities of interest. The quantities of interest aremore »