Abstract
This work generalises the application of functional expansion tallies to regular 2D and 3D geometries (derived from quadratic surfaces and extruded axially), based on orthogonal 2D polynomials in the unit disc. Zernike polynomials, as a special case of Jacobi polynomials, are selected as a basis for the analysis. The study describes the construction of the completeness set of polynomials based on an on-the-fly geometry-variable transformation methodology and particularises the approach to circle partitions and deformations. The results are evaluated against pre-calculated polynomials basis sets derived from Gram-Schmidt orthogonalisation process and bin-based reference solution.
| Original language | English |
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| Title of host publication | Mathematics & Computation (M&C) 2021 |
| Publisher | American Nuclear Society (ANS) |
| Pages | 239-248 |
| ISBN (Electronic) | 978-1-71388-631-0 |
| Publication status | Published - 2021 |
| MoE publication type | A4 Article in a conference publication |
| Event | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2021 - Virtual, Raleigh, United States Duration: 11 Apr 2021 → 15 Apr 2021 |
Publication series
| Series | Transactions of the American Nuclear Society |
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| Number | 3141 |
| ISSN | 0003-018X |
Conference
| Conference | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2021 |
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| Country/Territory | United States |
| City | Raleigh |
| Period | 11/04/21 → 15/04/21 |
Funding
This work was funded by Fortum & Neste Foundation (Finland), under grant agreement No. 20190207 (2019) and No. 20200149 (2020) - SMR Safety Analysis and Design Framework.
Keywords
- 2D geometry
- functional expansion tallies
- Monte Carlo
- Serpent 2
- Zernike polynomials