A New Method for the Doppler Broadening of the Solbrig’s Kernel Using a Fourier Transform

Ferran, Ghislain; Haeck, Wim; Gonin, M.

doi:10.13182/nse14-64

Cited by 10 publications

(24 citation statements)

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“…By leveraging a fast convolution method [8], an additional level of parallelism can be exposed, breaking each set into a smaller collections of independent operations. First, we observe (like some other modern methods, as in [9]) that the Doppler broadening equation (Eq. ( 1…”

Section: Novel Vectorized Methods Overviewmentioning

confidence: 61%

Gpu Acceleration of Doppler Broadening for Neutron Transport Calculations1

2021

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In radiation transport calculations, the effects of material temperature on neutron/nucleus interactions must be taken into account through Doppler broadening adjustments to the microscopic cross section data. Historically, Monte Carlo transport simulations have accounted for this temperature dependence by interpolating among precalculated Doppler broadened cross sections at a variety of temperatures. More recently, there has been much interest in on-the-fly Doppler broadening methods, where reference data is broadened on-demand during particle transport to any temperature. Unfortunately, Doppler broadening operations are expensive on traditional central processing unit (CPU) architectures, making on-the-fly Doppler broadening unaffordable without approximations or complex data preprocessing. This work considers the use of graphics processing unit (GPU)s, which excel at parallel data processing, for on-the-fly Doppler broadening in continuous-energy Monte Carlo simulations. Two methods are considered for the broadening operations – a GPU implementation of the standard SIGMA1 algorithm and a novel vectorized algorithm that leverages the convolution properties of the broadening operation in an attempt to expose additional parallelism. Numerical results demonstrate that similar cross section lookup throughput is obtained for on-the-fly broadening on a GPU as cross section lookup throughput with precomputed data on a CPU, implying that offloading Doppler broadening operations to a GPU may enable on-the-fly temperature treatment of cross sections without a noticeable reduction in cross section processing performance in Monte Carlo transport codes.

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Section: Novel Vectorized Methods Overviewmentioning

confidence: 61%

Gpu Acceleration of Doppler Broadening for Neutron Transport Calculations1

2021

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“…The temperature-optimized free Doppler kernel reconstruction method was tested on 238 U isotope data against linear interpolation, logarithmic interpolation, and the MCNP curve fit method discussed in section 4.1.3 for N = 2 through 15 reference temperatures. The results of this are displayed in figure (4). The free Doppler kernel reconstruction method was found to beat the other methods up to N = 12, at which point the maximum relative errors of the kernel reconstruction and the MCNP curve fit methods fell below the level of accuracy from the SIGMA1 Doppler broadening of the 238 U isotope data itself, rendering comparison meaningless.…”

Section: Performance Of Temperature-optimized Free Doppler Kernel Recmentioning

confidence: 97%

“…Boltzmann kernel reconstruction is rooted into Ferran's convolution formalization of the Doppler broadening operation [4]. Its Fourier analysis can help to physically justify the arbitrary choice of L 2 norm reconstruction using a frequency separation argument, as reported in appendix D. The algebraic solutions for the Boltzmann kernel reconstruction are derived in appendix C, and yield the following temperaturedependent systems:…”

Section: Boltzmann Kernel Reconstructionmentioning

confidence: 99%

“…Applying the Doppler broadening operation to s T yields a linear convolution product operator that transforms the generalized function s 0 from temperature T 0 to temperature T > T 0 as follows [4]:…”

Section: B12 Constrained Maxwell and Maxwell-over-velocity Kernels Rmentioning

confidence: 99%

“…Casting the Doppler broadening operation as a convolution with the Boltzmann distribution G. Ferran et al[4] recently introduced a generalized, odd parity, function s T linked to the cross section as:…”

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confidence: 99%

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Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

Ducru

Josey

Dibert

et al. 2017

Journal of Computational Physics

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This article establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j ). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature Tnamely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j ). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j ) is then undertaken so as to best reconstruct, in the L ∞ sense, the kernels over a given temperature range [T min , T max ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238 U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238 U total cross section over the temperature range [300K, 3000K] with only 9 reference temperatures.

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On-the-fly Doppler broadening method based on optimal double-exponential formula

Chen

Hao

et al. 2017

NUCL SCI TECH

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A New Method for the Doppler Broadening of the Solbrig’s Kernel Using a Fourier Transform

Cited by 10 publications

References 0 publications

Gpu Acceleration of Doppler Broadening for Neutron Transport Calculations1

Gpu Acceleration of Doppler Broadening for Neutron Transport Calculations1

Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

On-the-fly Doppler broadening method based on optimal double-exponential formula

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