Author Affiliations
1Institute of Applied Physics and Computational Mathematics, Beijing 100094, China2Graduate School of China Academy of Engineering Physics, Beijing 100088, Chinashow less
Fig. 1. Material temperature with different cell numbers (t = 10 ns).
Fig. 2. The convergence of material temperature: (a) Material temperature change with time in r = 0.05 cm; (b) material temperature change with cell number in r = 0.05 cm (t = 5 ns).
Fig. 3. The dependence of temperature on space is approxi-mately linear.
Fig. 4. Spatial probability density distribution of radiation source particle in different positions of radiation wave: (a) Cell 9, in the behind of wave; (b) cell 18, in the behind of wave; (c) cell 22, in the head of wave; (d) cell 26, in the head of wave.
Fig. 5. Material temperature with different cell numbers (t = 10 ns): (a) Multiplying sampling method; (b) stepped approximation sampling method.
Fig. 6. Results of two new sampling methods with 40 cells (t = 10 ns).
Cell number | Standard deviation/eV | Maximum error/eV | 20 | 80.8 | 273 | 40 | 48.7 | 254 | 100 | 28.9 | 245 | 200 | 13.0 | 125 |
|
Table 1. Relative to the reference solution, the standard deviation and the maximum error of temperature curves with different cell numbers.
Cell number | Particle number | Computation time/s | 20 | 1 × 104 | 1.80 × 103 | 40 | 2 × 104 | 2.72 × 103 | 100 | 5 × 104 | 5.74 × 103 | 200 | 2 × 105 | 2.28 × 104 | 400 | 4 × 105 | 5.06 × 104 |
|
Table 2. Computation time with different cell numbers.
Cell number | 乘抽样法 | | 阶梯近似抽样法 | Standard deviation/eV | Maximum error/eV | Standard deviation/eV | Maximum error/eV | 20 | 21.60 | 91.6 | | 18.80 | 77.8 | 40 | 13.60 | 75.4 | 12.40 | 68.7 | 100 | 10.40 | 77.9 | 10.40 | 87.6 | 200 | 5.64 | 63.3 | 5.27 | 59.5 |
|
Table 3. Relative to the reference solution, the standard deviation, and the maximum error of temperature curves with difference cell numbers.
Sampling method | Cell number | Particle number/104 | Computation time/103 s
| 等温法抽样 | 20 | 1 | 1.80 | 40 | 2 | 2.72 | 100 | 5 | 5.74 | 200 | 20 | 22.80 | 400 | 40 | 50.60 | 乘抽样法 | 20 | 1 | 1.65 | 40 | 2 | 2.56 | 100 | 5 | 5.64 | 200 | 20 | 22.40 | 阶梯近似抽样法 | 20 | 1 | 1.61 | 40 | 2 | 2.58 | 100 | 5 | 5.75 | 200 | 20 | 22.40 |
|
Table 4. Computation time of the problem.