Research And Application Of Spatial Modes Filtering FETD Method With Non-uniform Subgridding Mesh

When dealing with computational targets containing partial fine structures,the traditional finite-element time-domain(FETD)method suffers from limited computational efficiency due to the stability condition,where the time step is limited by the minimum spatial step.To address this issue,the spatial modes filtering FETD(SMF-FETD)method eliminates spatial modes that cannot be stably simulated at a given large time step,so that the system can iterate within the vector space of stable modes.The system instability is fundamentally eliminated.The SMF-FETD method liberates itself from the constraints faced by traditional FETD when dealing with partial fine structures and the time step is solely determined by the Nyquist theorem.However,it requires lots of computational resources(time and memory)to find unstable spatial modes through system generalized eigenvalue analysis,and the resource consumption is strongly related to the number of unknowns in the computational domain.Although the subgridding technique can reduce the number of unknowns,in order to enhance computational efficiency,it is still crucial to improve the relationship between the spatial discretization accuracy and the number of unknowns in the SMF-FETD method.Additionally,the current application scenarios of the SMF-FETD method are narrow,and its practical computational capability needs to be enhanced.Based on the basic framework of the SMF-FETD method,in response to the needs of the computational efficiency improvement and application scenario expansion,this work has carried out the following research:(1)A subgridding SMF-FETD method based on quadrilateral mesh is proposed.Aiming at the spatial discretization issues involving 2-D targets with partial fine structures,this method combines the advantages of non-uniform grids and subgridding technology to further reduce the number of unknowns while ensuring the accuracy of spatial discretization.The efficiency of system eigenvalue analysis is improved and the computational advantages of the SMF method are expanded.In contrast to traditional subgridding mesh distribution,in the nonuniform subgridding approach developed here,the number and length of fine edges at each subgridding coarse elements are non-uniform.The length of fine edges affects the reconstructed interpolation coefficients of the edge basis functions at the boundary,and the number of fine edges affects the size of the unit matrix formed by the the boundary coarse element.Flexible construction of unit matrices for subgridding coarse elements is a prerequisite to ensure the correctness of the system matrix combination.The development of non-uniform subgirdding approach further enhances the advantages of the SMF-FETD method and increases its computational efficiency.(2)A subgridding SMF-FETD method based on hexahedral mesh is proposed.Compared to quadrilateral mesh,the complexity of non-uniform subgridding approach based on hexahedral mesh is higher,and its implementation is more challengable.The grids with different scales are connected by element surfaces(interfaces).To ensure continuity of field values at interfaces,two schemes for exchanging informations of coarse and fine edges are proposed.These schemes differ in the transfer direction of edge field values and the reconstruction ways of edge basis functions.In the first scheme,the field values of coarse edge at the interface are represented by fine edges at the interface’s boundary.The value exchange process does not involve fine edges inside the interface,and the system matrices no longer contain coupling relationships related to coarse edges at the interface.In the second scheme,the basis functions of coarse edges at the interface are reconstructed by fine edges.The reconstruction coefficients are related to the distances between the fine edges and the coarse edges with same direction.All edges at the interface are involved in the field values exchange process,and the system matrices no longer contain coupling relationships related to fine edges at the interface.This work enhances the computational performance and practicality of the SMF-FETD method when dealing with 3-D targets with partial fine structures.(3)The SMF-FETD method for periodic structure is proposed and the differences in introducing periodic boundary condition(PBC)in 2-D and 3-D scenarios are explained.Periodic structures are common computational targets in electromagnetic simulation and have broad applications.However,the SMF-FETD method is less involved in the calculation of transmission characteristics analysis of such structures.Based on the Floquet theorem,PBC is introduced by incorporating the coupling relationship of periodic equivalent units into the system matrices.Subsequently,unstable spatial modes are extracted from the original numerical system to avoid the asymmetry of system matrices caused by PBC.In 3-D scenario,the absorbing boundary matrix has to be modified based on the equivalent information of PBC units.The periodic SMF-FETD method is combined with the computational advantages of non-uniform grids and subgridding mesh,conducting efficient simulations for typically periodic structure targets.The results validated the high efficiency and accuracy of the periodic SMF-FETD method.The in-depth research on the transmission characteristics of 2-D electromagnetic bandgap(EBG)structures and related influencing factors are conducted.By adjusting the dielectric parameters of the material,modifying the structural geometric parameters and introducing defect structures,the number and performance of stopbands of the EBG structure can be controlled.The practicality of the periodic SMF-FETD method is enhanced through transmission spectra calculation and analysis of 3-D metallic gratings and metal mesh array structures.