Time Domain Surface Integral Equation Method For Transient Electromagnetic Scattering Analysis

Electromagnetic scattering analysis techniques have been tremendously applied in areas such as radar dectection,target identification and electromagnetic compatibility analysis.Transient elemctromagnetic analysis has drawn growing propularity due to its unique benefits in analyzing electromagnetic phenomenons involving wide-band,time varying and non-linearity.This thesis has focused on applying the time domain surface integral equations(TDIEs)for transient electromagnetic scattering problems.It is devoted to the theory studies of the marching on in time(MOT)scheme for TDIEs.Stable,accurate and efficient time domain solvers have been implemented and employed for the transient scattering analysis of electrically large and multi-scale systems.The main contributions of this thesis have been summarized in following.(1)Starting from the time domain Maxwell's equation and its solution in free space,named time domain dyadic Green's function,we have established various time domain integral equations for both perfect electric conductors and homogeneous dielectrics.Characteristics of these integral equations,such as their Fredholm equation types,computational accuracy,computational stability and matrix conditioning,have been fully discussed and summarized,which lays the theoretical foundations for this thesis.(2)For the calculation of impulsive retarded potentials of impedance matrix exlements in TDIEs,a set of novel concise analytical formulae is proposed.Compared with previous analytical expressions,formulae in this paper can automatically catergorize the geometric relations between the field and source triangles.The tedious geometry calculations in traditional methods are no longer needed.The analytical evaluations of the impulsive retarded potentials can greatly improve the accuracy of coupling coefficients,which is necessary for accurate and stable MOT solvers in subsequent researches.(3)Propose a time domain augmented electric field integral equation(TD-AEFIE)to address the low frequency instabilities of the time domain electric integral equation(TD-EFIE).Compared with the traditional TD-EFIE,in the TD-AEFIE,a set of charge density unknowns are introduced based on the current continuity equation.Due to its excellent operator spectral property in low frequency,TD-AEFIE is an effective remedy for the low frequency instabilities of TD-EFIE.(4)The Loop and Flower basis functions are applied to get a low frequency stable TD-EFIE by implementing the Helmholtz decomposition.The Loop and Flower basis functions are both defined based on mesh nodes,and can be formed through linear combinations of the Rao-Wilton-Glisson(RWG)function.To get a well-posed equation,a temporally differentiated form of the TD-EFIE is tested with the flower function and the undifferentiated form is tested with the loop function.This scheme is very important to cure the low frequency instability of TD-EFIE.(5)This thesis proposes the time domain generalized transition matrix(TD-GTM)techinique and implements the substraction of the TD-GTM that contains scattering propertis of the targets.Transient scattering of multi-region systems are analyzed following the time domain generalized surface integral equation(TD-GSIE)scheme.The TD-GTM is established on the reference Huygens surface that encloses the object.The impulsive incidents are set on the reference surface,and the inside problem is analyzed using the MOT shceme.Then,we can get the convolutional relations between the in-going and out-going rotated tangential components of the electromagnetic fields.The benefits of TD-GTM such as order reduction,domain decomposition etc.,have been clearly demonstrated for analyzing transient scattering from large scale complex arrays of various objects.(6)A time domain discontinuous Galerkin surface integral(TD-IEDG)method is proposed,which employs the square-integrable function for the solution space of TDIEs.A novel time domain Galerkin weak formulation is established based on various penalty terms,making it possible to employ the non-conformal meshes for the electromagnetic computation.In the TD-IEDG method,the objects can be meshed independently part by part,according to its own geometric features.It provides an accurate and robust time domain integral equation solver with great flexibility and capability when dealing with wideband,multi-scale and electrically large problems.