Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

Goffin, Mark A.; Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.; Smith, Paul N.; Smedley-Stevenson, Richard P.

doi:10.1016/j.jcp.2014.10.063

Cited by 20 publications

(33 citation statements)

References 21 publications

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“…where f l,m are the expansion coefficients and Y l,m are the real, orthonormal spherical harmonics. If f is smooth, (3) will converge to to f with spectral accuracy as N → ∞. If f is not smooth, Gibbs oscillations will result and the approximation can result in negative solutions, which can be problematic in many applications.…”

Section: Spherical Harmonicsmentioning

confidence: 99%

“…where σ(η) is a filter function that obeys certain properties [10], including having a value of 1 on the isotropic moment, and that σ(η) only depends on l, making (4) rotationally invariant like (3). A strength parameter, s is also introduced into (4).…”

Section: Filtered Spherical Harmonicsmentioning

confidence: 99%

“…Performing adaptivity in the angular domain of the BTE is becoming more popular, as high angular resolution is required in many problems to resolve the streaming terms (i.e., when a particle propogates a long distance without interaction). Previously, in the AMCG we have investigated using several different angular discretisations with adaptivity across a range of different Boltzmann transport applications [1,2,3,4,5,6,7,8]. Recently [8] we showed scalable angular adaptivity implemented matrix-free with Haar wavelets that demonstrated O(n) scaling in both runtime and memory usage on some test problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Angular adaptivity with spherical harmonics for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2019

Journal of Computational Physics

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This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses P n and filtered P n expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically designed to use less memory than competing DG schemes and also gives us direct access to the amount of stabilisation applied at each node. For filtered P n expansions, we then use our adaptive process in combination with this net amount of stabilisation to compute a spatially dependent filter strength that does not depend on a priori spatial information. This applies heavy filtering only where discontinuities are present, allowing the filtered Pn expansion to retain highorder convergence where possible. Regular and goal-based error metrics are shown and both the adapted P n and adapted filtered P n methods show significant reductions in DOFs and runtime. The adapted filtered P n with our spatially dependent filter shows close to fixed iteration counts and up to high-order is even competitive with P 0 discretisations in problems with heavy advection.

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Section: Spherical Harmonicsmentioning

confidence: 99%

Section: Filtered Spherical Harmonicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Angular adaptivity with spherical harmonics for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2019

Journal of Computational Physics

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“…Our goal in the Applied Modelling and Computation Group (AMCG) has been to develop automated adaptive methods for general deterministic Boltzmann transport problems that are truly practical. Previously in the AMCG, we have investigated the use of spatial adaptivity, angular adaptivity, and combined space/angle adaptivity [1,2,3,4,5,6,7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Scalable angular adaptivity for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2020

Journal of Computational Physics

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This paper describes an angular adaptivity algorithm for Boltzmann transport applications which for the first time shows evidence of O(n) scaling in both runtime and memory usage, where n is the number of adapted angles. This adaptivity uses Haar wavelets, which perform structured h-adaptivity built on top of a hierarchical P 0 FEM discretisation of a 2D angular domain, allowing different anisotropic angular resolution to be applied across space/energy. Fixed angular refinement, along with regular and goal-based error metrics are shown in three example problems taken from neutronics/radiative transfer applications. We use a spatial discretisation designed to use less memory than competing alternatives in general applications and gives us the flexibility to use a matrix-free multgrid method as our iterative method. This relies on scalable matrix-vector products using Fast Wavelet Transforms and allows the use of traditional sweep algorithms if desired.

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“…The wavelet representation has certain advantages over the Pn and Sn representations in that streaming is not an issue and ray effects are less evident. Methods have been developed for goalbased space-angle adaptivity as illustrated in Figure 7 [59,60]. Figure 7a shows the adapted spatial mesh and how the order of the wavelet angular discretisation varies with spatial position.…”

Section: Adaptivitymentioning

confidence: 99%