Research On Fast PIC Simulation Based On Surface Impedance Boundary Condition

The Particle In Cell(PIC)method is a numerical simulation method to study the physical process of self-consistent interaction between electromagnetic fields and charged particles,which has important applications in the fields of military and national defense.The process of solving the electromagnetic field in the PIC method is usually carried out by the Finite Difference Time Domain(FDTD)method.When we use the FDTD method to solve complex electromagnetic problems,such as the electromagnetic field problem at the medium interface,fine meshing is often required.However,in order to satisfy the stability condition,the mesh should not be too fine.At this time,after the introduction of Surface Impedance Boundary Condition(SIBC),the coarse grid is directly used,and the study of the electromagnetic field inside the complex electromagnetic target is also avoided.Therefore the calculation process is simplified.This thesis studied the existing algorithms of "introducing SIBC into FDTD method",analyzed the advantages,disadvantages and applicable scope of various algorithms,and proposed a new algorithm with reference to the basic ideas of existing algorithms.The work of this thesis can be summarized as follows:1.Study the realization principle of SIBC in FDTD method,deduce the algorithm in detail and carry out numerical example analysis.This thesis firstly introduces the Maloney-Smith algorithm,which adopts the idea of "first transform in time domain and then approximate",which is computationally complex and inefficient.Then two simple and efficient algorithms are introduced,which named good conductor approximation algorithm and first-order rational approximation algrithm.Numerical example results show that the good conductor approximation algorithm is limited to the case of good conductors,while the first-order rational approximation algorithm has a wider range of applications.2.Referring to the idea of "first approximation and then time domain transformation",a Taylor expansion approximation algorithm is proposed.In this thesis,an ingenious Taylor expansion method is used to approximate the surface impedance.Compared with the first-order rational approximation algorithm,no complicated parameter calculation is required.This thesis have given the detailed derivation process and mathematical proof,and analyzed the error and computational complexity of the algorithm.Finally,a numerical example analysis is given.The results show that the Taylor expansion approximation algorithm has better accuracy than the first-order rational approximation algorithm in the case of low conductivity and high frequency.3.Implement the SIBC-FDTD algorithm with code,and couple it with other modules of fast PIC simulation,and add the surface impedance boundary function in the selfdeveloped simulation software Yuheng(Alioth).A simulation example analysis is given and compared with CST in this thesis.The correctness of the algorithm is verified from both microwave simulation module and charged particle simulation module,which indicate that SIBC-FDTD can provide a new solution for complex electromagnetic target analysis.