| Green’s function is a very vital concept in electromagnetic theory,the meaning of which is the response generated by a point source with unit intensity located at a point in space under certain boundary conditions.As can be seen from the definition,the Green’s function is related to the boundary conditions of the specific environment,so only under some certain specific boundary conditions,the Green’s function can be obtained in analytical form.For more general and complex boundary conditions,only traditional numerical methods such as the method of moments,finite-difference time-domain method,and the finite element method can be used to solve it with numerical form.Green’s functions obtained by numerical algorithms are generally called numerical Green’s functions and are often expressed in the form of matrix.When solved by numerical algorithms,Green’s function generally requires huge amount of operations and storage space,especially for complex three-dimensional scattering calculation scenarios.Therefore,it is very important for the development of the field of electromagnetic computing to find a way to solve the numerical Green’s functions more quickly and efficiently for three-dimensional scenarios.For the problem of solving numerical Green’s functions in three-dimensional scenes,this thesis proposes a neural network-based solution.Neural network is an algorithmic mathematical model with powerful fitting ability for complex information,which can achieve the purpose of processing information by adjusting the interconnection relationship of internal system nodes.Based on the physical definition of Green’s function,neural network is used in this thesis to approximate the functional relationship between the field source coordinate pair and the point source response in order to obtain the implicit numerical Green’s function.The content is divided into three stages to explain the specific work as below:First,the classical definition of numerical Green’s function and the relevant traditional numerical solving techniques are studied.Based on the definition and numerical solving methods of numerical Green’s function,this thesis introduced the neural network architecture representing numerical Green’s function.Second,this thesis investigates the neural network structure suitable for processing large amounts of data.Three-dimensional scattering scenes require more computational memory and time than two-dimensional scenarios since the amount of unknowns and data generated increases significantly,and a more complex neural network is required to handle the huge amount of operations.This thesis investigates the computational effects of various neural networks and adopts residual blocks into the deep neural network structure in order to avoid the degradation problem.Finally,the direct and scattering terms in the NGF are set apart according to the computational properties of matrix,changing the fitting target of the neural network into the relationship between the coordinates of the field and the source and the scattering terms;and then the neural network-accelerated three-dimensional numerical Green’s function can be calculated.Neural network require data to be of idetical distribution and independent.This extraction can makes the data in the training dataset more satisfying for this requirement,so that reduces the training burden of the neural network,which can make the neural network perform better in fitting function.This thesis also analyzed the advantages and limitations of the neural network algorithm applied in solving three-dimensional numerical Green’s function,and provides ideas for solving larger scale problems in the future. |
