Efficient Algorithms For Electromagnetic Computation

Computational electromagnetics is an interdisciplinary subject that brings together the knowledge of electromagnetics,computer science and numerical calculation methods.It provides theoretical and technical support for studying the ubiquitous electromagnetic phenomena in this day and age.Based on Maxwell’s equations,the electromagnetic forward analysis and inverse problem solving are two important parts of computational electromagnetic research.The forward problem can be summarized as solving Maxwell’s equations under given electromagnetic parameters,while the inverse problem always be abstract as searching for the corresponding electromagnetic parameters inversely in terms of the known electromagnetic response.Their high-efficiency and high-accuracy algorithms have always been a challenging but fascinating task in scientific engineering calculations.In view of some computational challenges encountered in forward problem and inverse problem in time-domain electromagnetics,this thesis combines traditional numerical simulation methods with machine learning to study fast and efficient solutions to electromagnetic problems.The main novelties and contents are as follows:(1)For the forward problems in electromagnetic scattering analysis,traditional DGTD numerical methods are usually limited by huge discrete degrees of freedom,especially for the analysis of parametric electromagnetic problems,leading to huge and unbearable computational cost.To improve computational efficiency,we design a non-intrusive reduced-order modeling(NIROM)algorithm(named POD-GPR algorithm)based on twostep proper orthogonal decomposition(POD)technology and Gaussian process regression(GPR)method.The data-driven method is used to approximate the nonlinear relationship between the reduced-order coefficients and the time-parameters,thereby realizing the complete decoupling between online query and offline physical modeling.The error analysis and numerical experiments show the effectiveness and superiority of the proposed algorithm,whose efficiency is much higher than that of the conventional DGTD method while ensuring high accuracy.(2)Dynamic tunable metasurface is an emerging technique used in the flexible control of electromagnetic waves.The relationship between its electromagnetic response and material parameters(such as dynamic susceptibility (?))is always characterized by the generalized sheet transition conditions(GSTCs).However,when it comes to the inverse problem of controlling and designing (?),GSTCs is usually difficult to be applied due to the complicated integration and division operations.In this thesis,we transform the inverse problem of solving dynamic (?) into a sequence control problem.Based on FDTD numerical simulation,a deep reinforcement framework(named GSTCs-PPO algorithm)using PPO algorithm and fully connected neural network is design to solving (?) intelligently and efficiently,which can find its value in assisting the design of the tunable metasurface,promoting further expansion of the application range of metasurface and thus helping realize more flexible and effective control of electromagnetic waves.The numerical results show the applicability,correctness and effectiveness of the proposed GSTCs-PPO algorithm.