Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

Conference · Fri Jul 01 04:00:00 EDT 2022

OSTI ID:23178668

Rosa, M. ^[1]

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1. The Pennsylvania State University, 113C Hallowell Building, University Park, PA 16802 (United States)

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

• Research Organization: American Nuclear Society - ANS, La Grange Park, IL 60526 (United States)
• OSTI ID: 23178668
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
DIFFUSION EQUATIONS
FOURIER ANALYSIS
FOURIER TRANSFORMATION
ITERATIVE METHODS