A Krylov-Schur solution of the eigenvalue problem for the neutron diffusion equation discretized with the Raviart-Thomas method

作者：Bernal Alvaro^*; Hebert Alain; Roman Jose E; Miro Rafael; Verdu Gumersindo

来源：Journal of Nuclear Science and Technology, 2017, 54(10): 1085-1094.

DOI：10.1080/00223131.2017.1344577

• Neutron diffusion equation
• finite element method
• Krylov-Schur
• Raviart-Thomas
• reactor physics

Mixed-dual formulations of the finite element method were successfully applied to the neutron diffusion equation, such as the Raviart-Thomas method in Cartesian geometry and the Raviart-Thomas-Schneider in hexagonal geometry. Both methods obtain system matrices which are suitable for solving the eigenvalue problem with the preconditioned power method. This method is very fast and optimized, but only for the calculation of the fundamental mode. However, the determination of non-fundamental modes is important for modal analysis, instabilities, and fluctuations of nuclear reactors. So, effective and fast methods are required for solving eigenvalue problems. The most effective methods are those based on Krylov subspaces projection combined with restart, such as Krylov-Schur. In this work, a Krylov-Schur method has been applied to the neutron diffusion equation, discretized with the Raviart-Thomas and Raviart-Thomas-Schneider methods.

• 出版日期2017