Research And Application Of Fast And Direct Solving Method Of Electromagnetic Integral Equation

With the continuous advancement of computer technology and the successive proposals of some fast algorithms,computational electromagnetics has developed rapidly in recent decades.The typical fast multipole algorithm has brought revolutionary applications to computational electromagnetics and laid the foundation for its development for more than two decades.Later,with the advent of some commercial simulation software,with the help of parallel computing acceleration,on today's personal computer,millions of unknown electromagnetic problems can be solved easily.But today's computational electromagnetics still has its development bottleneck.For example,in practical engineering applications,one of the primary problems faced by the simulation of electromagnetic characteristics of complex targets is that multi-scale structures are difficult to mesh conformally.Typically,such as the frequency select surface loaded on the radome,the antenna target on the electric large platform,etc.,it takes a lot of time to complete the preliminary integrated conformal meshing work.Moreover,the nonuniform grid generated by the multi-scale structure is easy to generate an ill-conditioned matrix,which will seriously affect the convergence speed.When the matrix is extremely ill-conditioned,it will even affect the accuracy of the direct solution.In addition,for some targets with strong coupling and strong resonance,such as air intakes and exhaust nozzles on airplanes,modern computational electromagnetics still faces the problem that traditional fast algorithm accelerated iterative solutions are difficult to converge.In the solution of a matrix problem with multiple right-hand sides,since each right-hand side needs to restart the process,the efficiency of iterative solution of traditional fast algorithms is not high.Typical examples are the calculation of the mono-static RCS of target and the dynamic simulation of the target's echo during the process of missile-target intersection.Aiming at the above engineering simulation problems,this paper proposes a direct solution method based on discontinuous Galerkin.This method introduces a mono-polar basis function,allows the target to be divided into regions and non-conformal divisions,and uses the discontinuous Galerkin method to discretize the integral equation to ensure the accuracy of the solution after the division.By allowing the target to set different meshing scales according to its geometric characteristics,the difficulty of integrated conformal meshing of complex structures is solved.Aiming at the problem of the nonconvergence of the traditional fast algorithm with strong coupling and strong resonance structure and the solution of the matrix problem with multiple right-hand sides,the direct solution method used in this paper first use the hierarchical matrices and the multi-level matrix decomposition algorithm to efficiently realize the sparse compression storage of the impedance matrix.Compared with the traditional low-rank compression algorithm,it can significantly reduce the storage resource consumption of the impedance matrix.Then a direct solution method based on hierarchical LU decomposition is constructed,which can quickly get the L and U matrices of the impedance matrix,and solve the problem that the traditional fast algorithm is not efficient in solving the ill-conditioned matrix and the multiple right-hand sides matrix problem.Experiments show that,compared with the traditional integrated meshing and iterative solution method,the direct solution method based on discontinuous Galerkin in this paper has the advantages of simple meshing,low memory consumption,and fast direct solution while ensuring the accuracy of the solution.It has a wide range of application prospects in the analysis of electromagnetic properties of complex multi-scale structures,the non-convergence problem of traditional iterative methods,and the solution of multiple right-hand sides matrix problems.