Study on algorithms for solving depletion sparse matrix based on DESCAR module

• Published in: Annals of nuclear energy Vol. 151; p. 107976
• Main Authors: Guo, Fengchen, Lu, Wei, Feng, Ziliang, Yu, Yang, Zeng, Hui
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2021
• Subjects: Calculation accuracy; Calculation efficiency; Depletion equation; Symbolic decomposition; Depletion equation; Calculation efficiency; Symbolic decomposition; Calculation accuracy
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2020.107976

•Several algorithms of solving sparse matrix are studied, including EDAGS, FSNZ etc.•ODFZ algorithm is proposed to improve the speed of solving depletion sparse matrix.•ODFZ has higher calculation accuracy and efficiency. Depletion solver with Chebyshev rational approximation method (DESCAR) was developed by Nuclear Power Institute of China (NPIC) to solve depletion equation. In this paper, the algorithms for solving depletion sparse matrix are studied, including symbolic Lower-Triangle and Upper-Triangle (LU) decomposition using elimination directed acyclic graphs (EDAGS), symbolic LU decomposition using symmetric reduction (FSNZ), symbolic LU decomposition using partial path-symmetric reduction (FPNZ), symbolic decomposition using elimination tree (ETREE), the direct sparse solver using pardiso routine in Intel math kernel library (PDMKL). An optimized direct factorization algorithm (ODFZ) is proposed to improve the speed of solving sparse matrix. The above methods are developed and tested in DESCAR module using a 17 × 17 pressurized water reactor (PWR) assembly containing Gd2O3-UO2 fuel rods. Results show that ODFZ method has highest calculation efficiency, the calculation speed is about 3.5 times that of PDMKL method.