Research And Application Of Efficient Numerical Method Based On Complex Source Point Beam

In the development of morden information technology,computational electromagnetics has been applied to and profoundly affects telemetry,remote sensing,wireless communication,nanotechnology and other areas.Innovative tools for new electromagnetic applications in all areas have always been one of the main tasks of computational electromagnetics.Among them,the fast and accurate solvers for multiscale problems attract many scholars' attention.As an exact solution to Maxwell's equations,the complex source point beam(CSB),which reduces paraxially to a Gaussian beam,has been widely used in the field of high frequency asymptotic methods.In recent years,along with the CSB expansion method for arbitrary electromagnetic fields,the CSB begins to emerge in the field of integral equations.With the application of the CSB to the integral equation,the cost of calculating far field coupling can be reduced by its natural directionality,and the multiscale problems can be effectively solved by the equivalent process.In this thesis,we focused on the acceleration of integral equations by CSB,as well as the efficient solution of multiscale problems.The research contents of this thesis are as follows:This thesis reviews the basic theory of the integral equation,summarizes the characteristics of CSB,introduces the equivalent principle of CSB for arbitary target,and deduces the far-field matching method of an arbitrary source.Further,the implementation details of the method to accelerate the electric field integral equation(EFIE)and the magnetic field integral equation(MFIE)are introduced.For the analysis of electrically large targets,the directionality and symmetry of CSB is used for the construction of an aggregation matrix,leading to the multilevel complex source beam method(MLCSB).The aggregation and translation method based on truncated singular value decomposition is proposed,which provided a compromise between accuracy and the computational efficiency by adjusting the threshold.In order to overcome the low-frequency breakdown of the electric field integral equation,the multilevel complex source point(MLCSP)method is proposed for the acceleration of augmented EFIE(AEFIE).The scalar and vector potential in AEFIE are expanded by scalar and vector potentials of CSP to avoid the low-frequency break problem in the equivalent process.Then,the matching method is used to generate an aggregation matrix and a multilevel algorithm.This method is proved to obtain O(N)computation complexity,and it is very stable in a wide frequency band.last but not least,an adaptive MLCSB is proposed,to solve multi-target problems.In this method,each target is divided separately using the oct-tree structure,a MLCSB routine is then applied for self-coupling,which results in the CSB expansion,and facilitates the direct translation coupling between targets of different size.A local aggregation method is also proposed to reduce the calculation of translation beams.In this thesis,the method of CSB and its application in integral equation are studied systematically and comprehensively.The directionality of CSB is utilized for the acceleration of method of moment,and the equivalence principle of CSB is exploited for multi-scale,multi-target and low-frequency problem.The research in this thesis provides new solution tools for integral equation method.