A Parallel Coloring Newton-Krylov Method for Multiphysics Coupling System in Nuclear Reactors

The Newton-Krylov method with the explicit Jacobian matrix is an efficient numerical method for solving the nuclear reactor nonlinear multiphysics coupling system. Compared with the Jacobian-free Newton-Krylov (JFNK) method, it has a better preconditioner matrix (the Jacobian matrix itself) and can achieve a more stable and faster convergence. How to compute the Jacobian matrix efficiently is a key issue for this method. The graph coloring algorithm is an essential technique and has been used to reduce the Jacobian computational burden by exploiting its sparsity. The fewer the coloring numbers in the Jacobian, the less the Jacobian computational cost will be. Besides, when computing the Jacobian in a distributed memory parallel environment, the parallel graph coloring algorithms are required because the Jacobian is distributed among processors. Currently, a popular parallel graph coloring algorithm has been used to color the Jacobian. However, this parallel graph coloring algorithm shows poor scalability in parallel. The coloring numbers will increase with the processors, resulting in poor Jacobian computational efficiency.