CAD-based FDTD Conformal Mesh And Its Application To The Simulation Of Optoelectronic Devices

In computational electromagnetics,the Finite-Difference Time-Domain method(FDTD)is widely used in electromagnetic computation and simulation due to its low programming complexity,simple mesh form,natural parallelizability,and time-domain-based algorithm.Since the Yee grid used by the FDTD method is a parallel hexahedral grid,it leads to the inability to fit the surface of a complex object as well as a tetrahedral grid,which inevitably causes large step errors.The conformal mesh technique can significantly reduce the step error by calculating the effective material coefficients of this mesh using the fill volume percentage of different materials within the mesh and the interface geometry information.The FDTD algorithm is generalized and can be applied to complex structures,but it also imposes higher requirements on mesh profiling.The analysis of complex graphic structures and the calculation of geometric information required for conformal meshes require a combination of computational graphics and computational electromagnetics.Therefore,this thesis addresses the need for generalized FDTD mesh profiling and delves into a conformal mesh profiling algorithm based on CAD(computer-aided design)files for triangular surface sheet modeling.Based on the characteristics of FDTD meshes,this paper also proposes a 3D FDTD conformal mesh generation algorithm based on CAD data,which realizes generalized and high-precision FDTD conformal mesh profiling combined with algorithms such as cropping and scanning in computational graphics.It also analyzes the CAD-based mesh generation algorithm in terms of complexity and fitness in conjunction with the FDTD algorithm with the research goal of reducing the spatial and temporal complexity of the conformal mesh generation algorithm and the spatial complexity of the FDTD algorithm;it deeply investigates the problems of reducing the spatial complexity of the conformal FDTD algorithm using computer graphics algorithms.The main research contents and innovative work are as follows:(1)This thesis investigates the method of mesh dissection using CAD files based on triangular surface element modeling,which achieves better compatibility with CAD software;it investigates the division method of generating the adaptive non-uniform mesh for the objective model based on the isometric approach,which can put limited computational resources in the critical area;it investigates the method of triangular surface element management based on spatial octree,which reduces the time complexity of triangular surface element indexing;in addition,it uses algorithms in computer graphics such as ray tracing algorithm,shadow volume algorithm,and separation axis theorem to complete the design and optimization of the conformal mesh generation algorithm.(2)This paper also investigates the CAD-based 3D FDTD conformal mesh generation algorithms,including volume-averaged conformal mesh,the Volume-average Polarized Effective Permittivity(VP-EP),and Contour Path Effective Permittivity conformal mesh,and proposes the Three Dimensional Contour Path Effective Permittivity(3D-CP-EP)generation algorithm based on generic CAD data,and further,the separation of conformalized and nonconformalized meshes in the mesh generation algorithm;(3)We propose a method to iterate the FDTD non-conformalized mesh and conformalized mesh separately.Based on the principle of full storage of non-conformal grid and sparse storage of conformalized grid,this paper investigates the method that can reduce the space complexity of complex conformal FDTD,which can effectively solve the problem that the iteration coefficients of complex conformal FDTD algorithm occupy too much memory.By comparing the proposed algorithm with the existing commercial FDTD software mesh profiling module in terms of profiling speed and mesh quality,the results show that the proposed conformal mesh error convergence speed is almost the same but occupies less computational resources,and the mesh generation speed is faster,and the speed of large-scale mesh profiling can be improved to more than 10 times compared with the same type of mesh profiling by Lumerical FDTD.