Research On Two-dimensional Electrostatic Particle Simulation Method Based On SuperLU

In the electromagnetic simulation software CHIPIC,the traditional electromagnetic PIC simulation method is adopted for the two-dimensional electrostatic module,that is,firstly,the grid area is divided according to the model,and the corresponding boundary conditions are imported for initialization,and then the initial particle is determined according to the emission model adopted by the particles.Particle charge distribution.In this process,the position of the particle is used to divide the charge into the surrounding four grid points.According to Maxwell’s equation,the electric field of the emitted particle is first calculated by using the charge distribution on each grid point,and then the solution is solved according to the electric field.A magnetic field is generated between the particles,and finally the current density between the particles is obtained according to the electric field and the magnetic field,so as to promote the movement of the particles and update the state of the particles.The above process is repeated until the corresponding conditions are met.However,the electromagnetic PIC simulation method used by CHIPIC has the problems of long calculation time and unstable calculation results when dealing with large-scale grids.And the electromagnetic PIC simulation method is constrained by the Courant stability criterion(where c is the speed of light and is the smallest cell size).As the grid size becomes smaller,the time step size also needs to be reduced,resulting in a surge in simulation time.The direct solution algorithm for two-dimensional electrostatic particle simulation proposed in this thesis mainly uses the direct solution method to solve the electric potential on all grid points at one time according to the charge distribution on each grid point.Harwell-Boeing’s compressed column storage format,because this format only stores the non-zero values of the coefficient matrix and related eigenvalues,solves the problem of large storage capacity and high computational complexity faced by traditional LU decomposition algorithms,thus greatly saving memory space.Then according to the potential difference,the electric field distribution in the x direction and the y direction can be obtained,and the corresponding particle motion can be driven according to the electric field distribution.In the simulation,the electromagnetic particle simulation method used by CHIPIC has the problems of long calculation time and unstable calculation results when dealing with large-scale grids.Moreover,the direct solution method can shorten the running time by controlling the time step and greatly improve the running efficiency.This thesis discusses the implementation steps of the calculation in detail,and demonstrates its practicability and accuracy through experiments.We also compare the algorithm with other traditional iterative algorithms and show the superiority of the algorithm.