Research On The Improved Absorbing Boundary Condition And Unconditionally Stable FDTD Method

The finite-difference time-domain(FDTD)algorithm has been widely studied in the field of electromagnetic computation since it was introduced,and has developed into a mature numerical calculation method.In the actual calculation problem,the problem of semi open and open area is usually encountered,however,the computational resources are limited,so the absorption boundary condition is critical to the cutoff of the FDTD region.In addition,the time step of the FDTD algorithm needs to satisfy the Courant-Friedrich-Levy(CFL)stability condition,which makes it less efficient in computing the simulation model with fine structures.Based on the above problems,the thesis of this paper focuses on the improvement of the absorption performance of the absorbing boundary conditions and the unconditionally stable FDTD method.Firstly,the paper gives a brief introduction to the basic knowledge of the FDTD algorithm and several classical perfect matched layer(PML)techniques.Then,an improved convolution perfect matching layer(CPML)technique is proposed to solve the non-synchronization problem of the fields value updating time in conventional CPML technique.Compared with the traditional CPML technology,the improved CPML has better absorption performance,higher computational efficiency,and without increasing the complexity of the CPML algorithm.Secondly,the unconditionally stable alternating-direction-explicit(ADI-FDTD)algorithm and the weak conditionally stable hybrid implicit-explicit(HIE-FDTD)algorithm are introduced,the time domain iterative formulas of the two algorithms are deduced after introducing the CPML absorption boundary,then,the iteration order of the components of the formula is given,the correctness and effectiveness of the CPML absorbing boundary in ADI-FDTD and HIE-FDTD algorithm are verified.Finally,an explicit unconditionally stable algorithm named spatially filtered FDTD(SF-FDTD)algorithm is introduced.Compared with the implicit FDTD algorithm,it does not need complex formula derivation and matrix inversion operation,which reduces the difficulty of the application of unconditional stability algorithm in FDTD method.The shortcoming of the traditional SF-FDTD method is that it can only be applied in the domain with the equal grid size in each direction,Based on this,an improved SF-FDTD algorithm is proposed which can be used in the area with unequal size in different positions,it enlarges the application scope of SF-FDTD method.Then,the SF-FDTD method is introduced into the subgridding technique,as the SF-FDTD method is not limited by CFL stability condition and we can choose larger time step according to coarse mesh to improve the computational efficiency.