| With the development of radar target detection and recognition technology,the analysis and calculation of radar cross section(RCS)has become the focus of attention.The study on a target's RCS is not only to obtain its scattering characteristics,but also to predict and optimize the future information system.Especially in recent years,since the stealth and anti stealth technologies are changing rapidly,more and more demands are made for the accurate calculation of RCS.However,the continuous increase of computing frequency in the actual application makes the electrical size of the target become larger.Besides,the detection targets are often located in half space environment.How to accurately and efficiently calculate the RCS of electrically large targets under limited computing resources has become a challenging problem.Based on this background,this dissertation takes the integral equation based multilevel fast multipole method(MLFMA)as the main research tool to study its parallel algorithms and domain decomposition method(DDM)to solve a series of engineering problems on supercomputers.Especially,DDM proposed in this dissertation can efficiently solve the scattering problem of electrically large targets in half space with enough precision guaranteed.This dissertation mainly studies the following aspects and has made some research achievements.The oct-tree formed by MLFMA is characterized by smaller number of non-empty tree nodes as well as larger number of plane waves at higher levels,while it shows the reverse trend at the lower levels.In order to improve the load balance of MLFMA on large-scale computer clusters according to its oct-tree structure,an adaptive partitioning strategy(Ad P)is proposed.For a non-empty tree node,its plane waves are assigned to the processes that share it,and hence the parallel efficiency is improved.In order to further solve the bottleneck that at the coarsest level the number of non-empty tree nodes are much smaller than parallel processors,a spatial partitioning strategy(SP)based on far-field approximation method is proposed.In this strategy,the coarsest level of an oct-tree is moved down from the second level to a lower level,and a hybrid of fast multipole method(FMM)and far-field approximation method is adopted at the new coarsest level.The advantages of Ad P and SP are dicussed through numerical examples.In addition,based on the micro architecture of modern computer,an optimized scheme that make full use of computer cache and vectorization unit is presented for the most time-consuming translation process in an MLFMA program.The optimized MLFMA program can achieve a speedup of 2.5 times and 4.6 times on CPU platform and new generation of many-core platform,respectively.In order to further enhance the capability of parallel MLFMA,an integral equation based non-overlapping domain decomposition method(IE-NDDM)using parallel MLFMA acceleration and Ad P as its parallel strategy is presented in this dissertation.For IE-NDDM,an explicit boundary condition for PEC problem is proposed,which not only enhances the continuity of electric currents that flow across the cutting contours between two subdomains but also satisfies that the inner electric field,charge accumulation and the electric potential are zero inside the PEC object.The troublesome singularity on the touching-faces of two adjacent subdomains is eliminated,and the convergence rate is improved when using GaussSeidel method.At the same time,the interface meshes are allowed to be non-conformal,providing unprecedented flexibility and convenience for mesh generation of complicated objects.To avoid the storage of the mutual impedance,different subdomains exchange the coupling in the manner of near field instead of traditional MLFMA with weight functions expanded in the disaggregation stage.The author also presents an MPI hybrid Open MP strategy to accelerate the matrix-vector multiplications of subdomains as well as the coupling between them.Numerical examples demonstrate that the proposed method is able to simulate realistic problems with a maximum dimension greater than 2000 wavelengths.Considering the impact of environments such as ground and sea,the parallel IE-NDDM is extended to half space situation.The implementation details and parallel strategy of MLFMA for half space environment are mainly studied.For the near interaction in half space,the discrete complex-image method(DCIM)is used similar to half-space Mo M.For the “reflected” terms of far interactions are evaluated via a real-image method.This method only introduces one set of real image clusters,which is favourable in stability and saves more memory consumption compared to the DCIM that introduces multiple complex images.Numerical examples show that the introduction of real image into IE-NDDM can accurately and efficiently analyze the scattering characteristics of electrically large targets in half space.In order to solve the problem of large formation in engineering applications,the SP parallel strategy is applied to the half space parallel IE-NDDM algorithm,and the scattering of tank formation on the ground and ship formation on the sea are successfully analyzed meeting the engineering accuracy requirement.According to the characteristics of MLFMA's hierarchical grouping,an oct-tree based domain decomposition method(OT-DDM)is proposed.In this dissertation,the whole model is partitioned adaptively based on the oct-tree structure of MLFMA.Each subdomain is a subtree of the whole oct-tree,and no additional interface is needed between subdomains,which greatly improves the convenience for processing the model.The coupling of the jagged buffer region between the two subdomains is computed via impedance method to eliminate higher order singularity,while the coupling of the rest regions are computed in the manner of field to reduce memory consumption.All computer resources focus on solving each subdomain and the scale of the problem to be solved is greatly enlarged.Numerical simulation results show that the method is of high pratical values. |
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