Integral Equation Methods And Applications In Multiple Scattering Problems

Aiming at solving the increasingly complex electromagnetic simulation problems,this dissertation thesis focuses on the integral equation method,making improvements on the broadband Green’s function theory,Foldy-Lax multiple scattering theory and high-performance electromagnetic numerical simulation technology.These theories are successfully applied to solve the eigenvalue problem of topological photonic crystals,and to low-frequency electromagnetic interference,successfully solving the TDD noise problem in mobile terminal equipment.The main contributions of this paper includes:(1)Development of the broadband Green’s function theory: The broadband Green’s function combined with the method of moments is applied to solve the eigenvalue problems of infinite periodic structures with various materials,including perfect electrical conductors,dielectrics,magneto-optical.Both 2D and 3D problems are studied.This makes the broadband Green’s function theory a complete theory for solving the eigenvalue problems of periodic structures with different dimensions and materials.The comparison with COMSOL simulation results validates the efficiency of the proposed method.(2)Breakthrough in rejecting spurious modes: This paper proposes a method to reject spurious modes by combining the combined field integral equation(CFIE)and the broadband Green’s function method.The electric field integral equation and the magnetic field integral equation are used to construct the combined field integral equation.With the help of the broadband Green’s function,the combined field integral equation is transformed into a linear eigenvalue problem.The eigenvalue only contains physical solutions,without spurious modes.This represents a huge leap in making the broadband Green’s function a practical technique for periodic scatterer scattering characterization.(3)Application of hybrid method: Taking advantages of integral equation method to deal with scattering problems of arbitrary structures and the efficiency of T-matrix method to calculate specific problems.Based on this method,the physical principle of topological one way edge mode is explained by using Green’s function and waveguide effect.(4)Mo M with machine learning: Combining the integral equation method with physicsinformed neural network(PINN)to predict scattering problem.The electromagnetic scattering problem is characterized by the method of moments,and the method of moments is transformed into a numerical optimization problem solved by the neural network using PINN.This method does not need to solve the matrix equation.With all the physical information required for scattering problem,the neural network can be trained without training dataset.The numerical results show the PINN can successfully predict the results of electromagnetic scattering problems.(5)Improvement of efficiency in numerical simulation: The partial element equivalent circuit(PEEC)method based on integral equation method is applied to solve the TDD noise problem in smart phones caused by low-frequency electromagnetic interference.The PEEC method is much more efficient in the co-simulation of field and circuit.For low-frequency electromagnetic simulation of complex structures,this paper proposes a method to simplify the model based on PEEC method to improve simulation efficiency.The good agreement of simulation and measurement validates the correction of this simplify method.The coupling current,combined with acoustic test in the anechoic chamber,is successfully used to predicted whether there is TDD noise for specific layout.