A GPU based iteration approach to efficiently evaluate radiation symmetry for laser driven inertial confinement fusion

• Published in: Applied Mathematical Modelling 2018-07, Vol.59, p.293-304
• Main Authors: Li, Haiyan, Huang, Yunbao, Jiang, Shaoen, Jing, Longfei, Xia, Hongjian, Huang, Tianxuan, Ding, Yongkun, Chen, Xin
• Format: Article
• Language: English
• Subjects: Cholesky factorization; Computation; Computer simulation; Decomposition; Flux density; Fusion; GPU; Heat conductivity; Inertial confinement fusion; Integration; iteration approach; Iterative methods; Laser Driven Inertial Confinement Fusion; Mathematical models; Parallel processing; Personal computers; preconditioned conjugate gradient; Radiation; Scale models; Symmetry
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2018.01.042

•Efficient computing approach presented for laser driven inertial confinement fusion•Guaranteed symmetry, strictly diagonally dominant and positive definite properties.•GPU based Preconditioned Conjugate gradient iteration approach.•The radiation models are efficiently solved and validated with two examples. Radiation computation is very important for high energy density experiments design in the laser-driven Inertial Confinement Fusion. The view-factor based models are often used to calculate the radiation on the capsule inside a hohlraum. However, it usually takes much time to solve them when the number of equations is very large. In this paper, an efficient iteration approach GPU is presented. The core idea is: (1) guaranteed symmetry, strictly diagonally dominant, and positive definite properties underlying the models are described, (2) a preconditioned conjugate gradient iteration approach is presented to compute the radiation based on such guaranteed properties, and (3) such approach is then parallelized and implemented for GPU so that the large scale models, especially for the non-linear model, can be efficiently solved in reasonable time. Finally, two experimental targets for Shenguang laser facilities built in China are demonstrated and compared to validate the efficiency of the presented approach. The results show that, the models’ computation (1) can be speeded up with successive over-relax iteration method by eight times as compared with Cholesky factorization based direct approach, (2) can be accelerated more with the preconditioned conjugate gradient iteration approach by almost eight times, and (3) can be further accelerated about 2 to 4 times as it parallelized and run on the GPU, which enables the large scale models, can be efficiently solved in reasonable time on the usual desktop computers.