An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems

The heterogeneous variational nodal method (HVNM) has emerged as a potential approach for solving high-fidelity neutron transport problems. However, achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs. This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard. The algorithm evenly distributes the response matrix sets among processors during the matrix formation process, thus enabling independent construction without communication. Once the formation tasks are completed, a collective operation merges and shares the matrix sets among the processors. For the solution process, the problem domain is decomposed into subdomains assigned to specific processors, and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation. Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries. The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases. Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations. The parallelization of HVNM results in eigenvalue errors of 31 pcm/\(-\)90 pcm and fission rate RMS errors of 1.22%/0.66%, respectively, for the 3D KAIST problem and the 3D JRR-3 problem. In addition, the parallel algorithm significantly reduces computation time, with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem.