The 6th International Conference on Matter and Radiation at Extremes (ICMRE2023)

228 / 2023-04-17 13:01:20

VSHPIC: A highly efficient three-dimensional parallel particle-in-cell code based on vector spherical harmonics expansion

PIC algorithm, vector spherical harmonics, mode decomposition

Radiation and Hydrodynamics > Radiation and hydrodynamics-poster

As one of the important computational methods for studying plasma physics, the Particle-in-Cell (PIC) method can self-consistently simulate the motion of a large number of charged particles in a plasma under the combined influence of their self-fields and external fields. Moreover, this algorithm enables scalable parallelization, which makes it a widely used scientific computing program on various supercomputers. Although PIC programs can be parallelized, three-dimensional PIC simulations of certain physical problems still require significant computational resources. To reduce the computational load while preserving three-dimensional characteristics in the physics problem, a PIC algorithm based on the mode decomposition was proposed and initially applied in cylindrical coordinate systems ^[1,2]. The method described in references [1,2] expands the fields into Fourier series in the azimuthal (φ) direction, which reduces the three-dimensional problem to a two-dimensional (or quasi-three-dimensional) problem. It can greatly reduce the number of simulated particles and thus decreases computational burden and saves computation time. In this work, we introduce a novel PIC code VSHPIC , which is based on the mode decomposition in the spherical coordinates. Instead of Fourier expansion, we expands all the physical quantities by using vector spherical harmonics, which are in θ and φ directions. This allows us to reduce the three-dimensional problem to a one-dimensional problem. The code can simulate three-dimensional asymmetric problems by keep tracking the evolution of different individual modes. Due to the less simulated particles we need in the code, the computational load of VSHPIC for the same physical problem will be significantly decreased compared to regular PIC programs.



References

[1] A. F. Lifschitz, X. Davoine, E. Lefebvre et al., Journal of Computational Physics 228, 1803–1814 (2009).

[2] A. Davidson, A. Tableman, W. An, et al., Journal of Computational Physics 281, 1063–1077 (2015).