Iterative convergence acceleration of neutral particle transport methods via adjacentcell preconditioners
Abstract
The author proposes preconditioning as a viable acceleration scheme for the inner iterations of transport calculations in slab geometry. In particular he develops AdjacentCell Preconditioners (AP) that have the same coupling stencil as cellcentered diffusion schemes. For lowest order methods, e.g., Diamond Difference, Step, and 0order Nodal Integral Method (ONIM), cast in a Weighted Diamond Difference (WDD) form, he derives AP for thick (KAP) and thin (NAP) cells that for model problems are unconditionally stable and efficient. For the FirstOrder Nodal Integral Method (INIM) he derives a NAP that possesses similarly excellent spectral properties for model problems. The two most attractive features of the new technique are:(1) its cellcentered coupling stencil, which makes it more adequate for extension to multidimensional, higher order situations than the standard edgecentered or pointcentered Diffusion Synthetic Acceleration (DSA) methods; and (2) its decreasing spectral radius with increasing cell thickness to the extent that immediate pointwise convergence, i.e., in one iteration, can be achieved for problems with sufficiently thick cells. He implemented these methods, augmented with appropriate boundary conditions and mixing formulas for material heterogeneities, in the test code APID that he uses to successfully verify the analytical spectral properties for homogeneous problems. Furthermore, he conductsmore »
 Authors:
 Oak Ridge National Lab., TN (United States)
 Publication Date:
 OSTI Identifier:
 361773
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 152; Journal Issue: 1; Other Information: PBD: 10 Jun 1999
 Country of Publication:
 United States
 Language:
 English
 Subject:
 66 PHYSICS; ITERATIVE METHODS; CONVERGENCE; NEUTRALPARTICLE TRANSPORT; BOUNDARYVALUE PROBLEMS; SPECTRA UNFOLDING
Citation Formats
Azmy, Y.Y. Iterative convergence acceleration of neutral particle transport methods via adjacentcell preconditioners. United States: N. p., 1999.
Web. doi:10.1006/jcph.1999.6251.
Azmy, Y.Y. Iterative convergence acceleration of neutral particle transport methods via adjacentcell preconditioners. United States. doi:10.1006/jcph.1999.6251.
Azmy, Y.Y. Thu .
"Iterative convergence acceleration of neutral particle transport methods via adjacentcell preconditioners". United States.
doi:10.1006/jcph.1999.6251.
@article{osti_361773,
title = {Iterative convergence acceleration of neutral particle transport methods via adjacentcell preconditioners},
author = {Azmy, Y.Y.},
abstractNote = {The author proposes preconditioning as a viable acceleration scheme for the inner iterations of transport calculations in slab geometry. In particular he develops AdjacentCell Preconditioners (AP) that have the same coupling stencil as cellcentered diffusion schemes. For lowest order methods, e.g., Diamond Difference, Step, and 0order Nodal Integral Method (ONIM), cast in a Weighted Diamond Difference (WDD) form, he derives AP for thick (KAP) and thin (NAP) cells that for model problems are unconditionally stable and efficient. For the FirstOrder Nodal Integral Method (INIM) he derives a NAP that possesses similarly excellent spectral properties for model problems. The two most attractive features of the new technique are:(1) its cellcentered coupling stencil, which makes it more adequate for extension to multidimensional, higher order situations than the standard edgecentered or pointcentered Diffusion Synthetic Acceleration (DSA) methods; and (2) its decreasing spectral radius with increasing cell thickness to the extent that immediate pointwise convergence, i.e., in one iteration, can be achieved for problems with sufficiently thick cells. He implemented these methods, augmented with appropriate boundary conditions and mixing formulas for material heterogeneities, in the test code APID that he uses to successfully verify the analytical spectral properties for homogeneous problems. Furthermore, he conducts numerical tests to demonstrate the robustness of the KAP and NAP in the presence of sharp mesh or material discontinuities. He shows that the AP for WDD is highly resilient to such discontinuities, but for INIM a few cases occur in which the scheme does not converge; however, when it converges, AP greatly reduces the number of iterations required to achieve convergence.},
doi = {10.1006/jcph.1999.6251},
journal = {Journal of Computational Physics},
number = 1,
volume = 152,
place = {United States},
year = {Thu Jun 10 00:00:00 EDT 1999},
month = {Thu Jun 10 00:00:00 EDT 1999}
}

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