Imperial College London
Dr Matthew Eaton

DrMatthewEaton

Faculty of Engineering, Department of Mechanical Engineering

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+44 (0)20 7594 7053m.eaton

 
 
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Location

 

657City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{O'Malley:2016:10.1016/j.anucene.2016.11.048,
author = {O'Malley, B and Kophazi, J and Smedley-Stevenson, RP and Eaton, MD},
doi = {10.1016/j.anucene.2016.11.048},
journal = {Annals of Nuclear Energy},
pages = {134--147},
title = {Hybrid multi-level solvers for discontinuous Galerkin finite element discrete ordinate (DG-FEM-SN) diffusion synthetic acceleration (DSA) of radiation transport algorithms},
url = {http://dx.doi.org/10.1016/j.anucene.2016.11.048},
volume = {102},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - his paper examines two established preconditioners which were developedto accelerate the solution of discontinuous Galerkin  nite element method (DG-FEM) discretisations of the elliptic neutron di usion equation.  They are eachpresented here as a potential way to accelerate the solution of the Modi ed In-terior Penalty (MIP) form of the discontinuous di usion equation, for use as adi usion synthetic acceleration (DSA) of DG-FEM discretisations of the neutrontransport equation.  The preconditioners are both two-level schemes, di eringin the low-level space utilised.  Once projected to the low-level space a selectionof algebraic multigrid (AMG) preconditioners are utilised to obtain a furthercorrection step, these are therefore \hybrid" preconditioners.  The  rst precon-ditioning scheme utilises a continuous piece-wise linear  nite element method(FEM) space, while the second uses a discontinuous piece-wise constant space.Both projections are used alongside an element-wise block Jacobi smoother inorder to create a symmetric preconditioning scheme which may be used along-side a conjugate gradient algorithm.  An eigenvalue analysis reveals that bothshould aid convergence but the piece-wise constant based method struggles withsome of the smoother error modes.  Both are applied to a range of problems in-cluding some which are strongly heterogeneous.  In terms of conjugate gradient(CG) iterations needed to reach convergence and computational time required,both methods perform well.  However, the piece-wise linear continuous schemeappears to be the more e ective of the two.  An analysis of computer memoryusage  found  that  that  the  discontinuous  piece-wise  constant  method  had  thelowest memory requirements.
AU  - O'Malley,B
AU  - Kophazi,J
AU  - Smedley-Stevenson,RP
AU  - Eaton,MD
DO  - 10.1016/j.anucene.2016.11.048
EP  - 147
PY  - 2016///
SN  - 1873-2100
SP  - 134
TI  - Hybrid multi-level solvers for discontinuous Galerkin finite element discrete ordinate (DG-FEM-SN) diffusion synthetic acceleration (DSA) of radiation transport algorithms
T2  - Annals of Nuclear Energy
UR  - http://dx.doi.org/10.1016/j.anucene.2016.11.048
UR  - http://hdl.handle.net/10044/1/42923
VL  - 102
ER  -
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