Research On Target Electromagnetic Scattering Characteristics Based On Hierarchical Matrix

The discipline of computational electromagnetics has been developed with the extensive application of electromagnetics.The method of moments in computational electromagnetics is well received by researchers because of its high precision and its own integral equations that satisfy boundary conditions without generating dispersion errors.Love.However,when the moment method calculates the electromagnetic scattering of the target,a full-rank impedance matrix is formed,which leads to the problem that the calculation amount is too large and the storage amount is too large when calculating the scattering of the electric large-size target by the moment method.This paper seeks an improved algorithm of the moment method to speed up the calculation.This paper first introduces the calculation method of the moment method of calculating the target scattering method,including the principle of the moment method,geometric modeling,selection of basis function and weight function,establishment of integral equation and how to solve the concept of "moment" Integral equation.The calculation process of radar cross section in 2D and 3D problems is given,and the algorithm is verified by conductor cylinder and conductor ball.In order to accelerate the calculation of the moment method,the idea of layered matrix is introduced.The impedance matrix of the system is divided into an admissible matrix and an unacceptable matrix according to whether the obligate condition is satisfied.The admissible matrix will continue to be divided according to the conditions.Until the lowest base function of the tree structure is less than the threshold.In this way,the impedance matrix of the system is divided into several small matrix blocks,and then the matrix blocks are calculated by the Lagrange interpolation polynomial method.In order to avoid the generation of the Runge phenomenon in the calculation process,the Chebyshev method is used to generate the interpolation point.This method of layering matrix can effectively reduce the amount of calculation of the moment method,and the error of the impedance matrix is within the controllable range.Finally,by considering the hierarchical matrix as the preprocessing of the moment method,the hierarchical matrix is combined with the adaptive crossapproximation algorithm and the multi-layer fast multipole algorithm to accelerate the hierarchical matrix.In the adaptive cross-approximation algorithm,a new method for evaluating the convergence criterion,the Frobenius norm,is proposed.The number of iterations required for relative error should be minimized as accurately as possible in the ACA,assuming that the absolute residual error at each iteration is the latest update of magnitude,but for an oscillating kernel,sometimes it cannot be achieved due to its erroneous rotation.This,even in extreme cases,may cause the algorithm to converge before it has been implemented,and the oscillating kernel will generate additional computations each time it is updated,seriously affecting the efficiency of the solution.This new method effectively reduces the computation time and the probability that the estimated parameters will have unacceptable results will be almost zero.