Research On Domain Decomposition Method Of Integral Equation Discontinuous Galerkin

The analysis of the electromagnetic characteristics from large-scale and multi-scale targets has always been the focus of computational electromagnetics.If the method of moments(MoM)is used to perform simulation analysis on such targets,the conformal mesh can only be obtained by integrated dissection,and the model is often not well fitted,so that problems such as poor matrix condition numbers and difficult iterative convergence will occur.The domain decomposition method can effectively solve the large-scale problem,which transforms the surface integral equation problem into subdomain problems.The discontinuous Galerkin method further allows the grid to be non-conformal,thereby solving the multi-scale problem.In this regard,this paper has carried out the research of discontinuous Galerkin domain decomposition method based on integral equation.The research contents can be divided into the following parts:1.A discontinuous Galerkin method based on the augmented electric field integral equation(AEFIE-DG)is studied,which can flexibly and efficiently calculate the electromagnetic scattering characteristics of multi-scale targets.Based on the discontinuity of the surface current,the surface charge and the linear charge are introduced separately.The non-uniform meshing cannot guarantee the normal continuity of the current across the subdomain boundary,which will cause the accumulation of error charges at the subdomain boundary.Therefore,the current Robin transmission condition is introduced at the discontinuous boundary and combined with the current continuity equation to obtain the augmented electric field integral equation(AEFIE).This method uses non-conformal grid cells to geometrically model the target,and uses grid cells of different sizes in different geometric structures of the multi-scale model,which greatly improves the flexibility of grid discreteness.2.A discontinuous Galerkin domain decomposition method weighted by method of moments(MoM-DG-DDM)is studied,which is used to solve large-scale and multi-scale problems.The surface integral equation problem is transformed into subdomain problems.As for the error charge accumulated at the discontinuous boundary,the internal penalty term is determined by making the error potential energy zero,thereby obtaining the discontinuous Galerkin method based on combined field integral equation(CFIE-DG).The solution process of the domain decomposition method weighted by method of moments(MoM-wDDM)is divided into three steps: the first step is to directly solve each subdomain problem without considering mutual coupling;the second step is to linearly combine all subdomain solutions of previous and current iterations with the weights determined by MoM for the final solution of this step;the third step is to find the residuals of the final solution of this step relative to the original surface integral equation problem to use as an incentive in the next iteration.This method can achieve non-conformal meshing of complex structures in multi-scale problems,and has the characteristics of rapid convergence.It only requires a few steps or dozens of iterations to obtain more accurate results,which can effectively solve the problem of electromagnetic scattering of targets with large-scale and multi-scale.3.Applying the discontinuous Galerkin domain decomposition method weighted by method of moments(MoM-DG-DDM)to solve the radiation problem of array antennas.Based on the calculated far-field radiation patterns,the fault diagnosis method of array antennas based on deep learning is studied.A trainable convolutional neural network model is used to automatically extract features,and a trainable fully connected neural network is used to classify the failure modes.The Adam optimization algorithm is used to train the overall deep neural network model.This method not only avoids the trouble of manually extracting features,but also greatly improves the accuracy of fault diagnosis.For a dipole array antenna with 100 elements,the accuracy of fault diagnosis can reach 97.4% when the signal-to-noise ratio is 10 dB.