Efficient Electromagnetic Simulation Algorithms For Multiscale Complex Scenes

With the rapid development of electromagnetic theory algorithms and computer technology,the application of computational electromagnetism in scientific research and real life is more and more extensive.And the electromagnetic simulation tools for realistic complex scenes need higher and higher requirements on the accuracy and efficiency.According to the ratio between the geometric size of a scene and wavelength of simulation wave,also known as the electrical size,electromagnetic scenes can be divided into two categories:electrically large and electrically small.Electromagnetic simulation algorithms are faced with different complex problems in different electrical sizes of scenes.For example,in electrically small scenes,electromagnetic objects have fine and complex geometric structures,or inhomogeneous anisotropic materials,or multi-element periodic structures or other characteristics,which often needs to be solved by accurate low-frequency numerical algorithms.While in electrically large scenes,the large-scale electromagnetic environments are complicated and changeable,such as,shadowing by trees and vegetation with seasonal changes in ground environment,dense buildings and various materials in urban environment,which often makes the high-frequency asymptotic methods more suitable for the simulation and modeling in such electromagnetic environments.In the face of the above challenges,this thesis focuses on the efficient electromagnetic simulation algorithms for multiscale complex scenes.Different electromagnetic algorithms are used for simulation of scenes with different scales.In the electrically small scenes,the electromagnetic scattering characteristics of complex objects are studied,and the numerical performance of the method of moments(MoM)in low frequency for analyzing periodic structure objects and inhomogeneous lossy medium objects is improved.In the electrically large scenes,the radio propagation models of complex urban environment are studied,and the signal propagation simulation systems based on high-frequency asymptotic methods with modeling of surface elements and point cloud are optimized.For different-scale scenes,the efficiency of the electromagnetic simulation algorithms in thesis are improved greatly under the condition of reliable accuracy.Firstly the basic theories of electromagnetic algorithms in frequency domain are introduced.As the core algorithms,both MoM of integral equations and the shooting and bouncing ray(SBR)of the high-frequency asymptotic methods are emphatically introduced,which run through this thesis.For MoM,the precision and the difficulty of implementation by three types of singularity extraction techniques,namely Duffy transform,projection integration and analytic integration,are analyzed in detail.Furthermore,MoM is accelerated by the classical method,the multi-level fast multipole algorithm(MLFMA).And the Lagrange interpolation,bicubic interpolation and the bilinear interpolation methods in MLFMA are deduced and their advantages and disadvantages are compared.Then two forms of ray tube in SBR which are quadrangular prism and pyramid,as well as the existing mainstream acceleration and optimization strategies of SBR are described briefly.In order to solve the periodic structures fast,the MoM accelerated by the pseudo-skeleton approximation(PSA)algorithm is proposed.A reasonable estimate of the rank of the decomposed matrix in PSA is given first,and appropriate rows and columns are selected in a way similar to adaptive cross approximation(ACA)algorithm.Then the internal self-coupling and external mutual-coupling matrixes of the periodic elements are accelerated by PSA for the entire periodic structures.What's more,the displacement invariance is applied to minimize the number of mutual-coupling matrix blocks.Whether computation for loose or tight coupling or large-scale periodic structures,the PSA-based MoM method in this thesis achieves superior computational efficiency and extremely low memory usages compared with the traditional MLFMA under the condition of ensuring accuracy error.To deal with the inhomogeneous lossy dielectric objects,the volume integral equations(VIE)based on the discontinuous Galerkin method is exploited.The SWG basis function to expand impedance matrix on discontinuous boundaries is explained in detail.Before constructing the SWG pairs,a new method based on map associative container is proposed which greatly improves the efficiency in the early stage of simulation.Since a large number of unknown are generated from the volume mesh in VIE,it is in urgent request for acceleration by MLFMA.However MLFMA suffers from the low-frequency breakdown problem when dealing with over-meshed objects.Therefore a hybrid strategy of MLFMA-ACA is proposed which gives full play to the stability of ACA in low frequency and the efficiency of MLFMA in high frequency.In addition,the volume surface integral equation method is implemented in this thesis which expands the ability of analyzing the electromagnetic scattering characteristics of objects with metal-dielectric composite structures.Next,aiming at the radio propagation model in complex urban environment,the beam tracing(BT)method based on triangular-facet model is developed.To solve the drawback of beams in diffraction,an approximate method of virtual equivalent sphere is proposed.This method only uses beams without rays throughout the entire process and can compute any combination paths of signals.Moreover,by making use of the independence of different beams,the GPU parallel acceleration for BT model has been implemented.And the trees and vegetation in outdoor environment are modeled and the transmission attenuation effect of them on the signal is reasonably considered for the first time,which improves the simulation accuracy of BT model in real scenarios.Finally,in the face of the emerging modeling method for urban scenes which uses point cloud data,the electromagnetic algorithm based on point cloud for fast channel response is investigated.In allusion to the shortcomings of the existing models,the estimation for normal vector and effective area in diffuse scattering model,and the error problem of calculating Fresnel area coefficient in specular reflection model are improved and optimized.And the diffraction edges are extracted automatically for the diffraction model as well.Furthermore,octree structure is employed to realize the efficient management and shadowing detection of point cloud.And after clustering and extraction of the trees and vegetation in point cloud,the attenuation of signals through trees is considered,which improves the accuracy of the simulation model.For different-scale scenes,in view of the difficulties and challenges for different types of complex targets and different modeling data of complex urban environment in electromagnetic simulation,this thesis carries out in-depth analysis and discussion and improved the shortcomings or defects of the existing algorithms.A large number of numerical examples demonstrate that the efficiency of simulation systems in this thesis can be greatly improved with reliable accuracy.