Fast Solution Of Scattering Of Complex Cavity Structure Based On Direct Solver

Solving the scattering characteristics of complex cavities and targets containing cavities has long been one of the most important and challenging topics in computational electromagnetics(CEM).The cavity structure is the part with strong scattering on the aircraft.Carrying out the electromagnetic scattering research of cavity-type targets is pretty important for understanding the electromagnetic wave propagation mechanism in the cavity,the design of the cavity shape and structure,and the performance of the cavity-type stealth materials.The electromagnetic integral equation method,as an efficient full-wave numerical method,only needs to be geometrically discrete on the target surface or the target's own region,the mesh is flexible,and the calculation result is accurate.However,when the integral equation method is used to solve the electromagnetic scattering characteristics of the cavity problem,the electromagnetic wave will resonate inside the cavity and the coupling is very strong.These will cause the impedance matrix to be very ill-conditioned.In the analysis of cavity target scattering,the condition number of the matrix formed after the discretization is large,the iterative method has very poor convergence,and cannot deal with the bottleneck problems such as multiple right-hand sides.We will adopt the direct solver to avoid it.Skeletonization is an efficient and fast direct solution algorithm.It mainly uses Interpolative Decomposition(ID)to select some rows and columns of the original system matrix,and use a sparse data format to approximate the full storage.This completes the compression and decomposition of the matrix.This algorithm is very beneficial to the analysis of the scattering characteristics of electrically large and complex cavity structures.First of all,based on the skeletonization algorithm,this paper uses Huygens principle to select the appropriate equivalent surface in the compression process of the system matrix,and then uses the sampling of some specific points on the equivalent surface to avoid the discretization of the entire equivalent surface.This method can greatly reduce the number of basis functions,reduce the dimensionality of the system matrix,and realize further compression of the system matrix,which is beneficial to the study of the scattering characteristics of complex cavity targets.Then,through the analysis and comparison of the calculation results of the scattering characteristics of the two types of typical open cavity,this paper selects the ID tolerance parameters suitable for the solution of the cavity target.The accuracy and effectiveness of the algorithm are verified by comparing the numerical calculation results and measurement results of a specific cavity structure under four different incident frequencies.Next,this paper has completed the geometric modeling of the four types of strong representative cavity structures,and completed the calculation of their scattering characteristics using the skeletonization algorithm.The results show that the skeletonization algorithm is more accurate and efficient than the traditional iterative method.Finally,this paper studies the contribution of the cavity opening size and terminal opening and closing to the overall scattering characteristics of the target.Then,the influence of the cavity shape on the overall scattering of the target is verified by calculating the scattering characteristics of the whole target.It provides useful numerical results for the design of cavity targets such as intake ducts.