Reseach On Marching-on In-time Scheme And The Fast Algorithm Of Time Domain Integral Equation

With the widespread engineering applications ranging from broadband signals andnon-linear systems, time-domain integral equations (TDIE) methods for analyzingtransient electromagnetic scattering problems are becoming widely used nowadays.TDIE-based marching-on-in-time (MOT) scheme and its fast algorithm are researchedin this dissertation, including the numerical techniques of MOT scheme, late-timestability of MOT scheme, and two-level PWTD-enhanced MOT scheme. The contentsare divided into four parts shown as follows.Firstly, the foundational theory of TDIE-based MOT scheme is reviewed. Byderiving from the time-domain Maxwell Equations, the time-domain electric fieldintegral equation (TDEFIE), the time-domain magnetic field integral equations(TDMFIE), the time-domain combined field integral equation (TDCFIE), and the MOTscheme for solving TDIE are obtained. The computational precision and complexity ofTDIE-based MOT scheme are analyzed theoretically. Meanwhile, common spatial basisfunction and time basis function used for numerical discretization of TDIE, and incidentwave of time-domain pulse style, are also introduced.Secondly, the important numerical techniques of TDIE-based MOT scheme areexplored. With the improvements of the computation method for impedance elements,the memory method for storing impedance matrix, the solution for matrix equations andthe discretization for integral equations, the MOT scheme of high precision andefficiency has been achieved. First of all, the method of DUFFY transformation and themethod of precise computation based on convolution integral are both applied tocalculate time-domain impedance elements, which can ensure the computationalprecision of TDIE-based MOT scheme. Then, considering the characteristics ofimpedance matrix produced by TDIE-based MOT scheme, a new method formemorizing the impedance matrix is proposed to enhance the memory efficiency. Next,methods of directive and iterative solutions respectively used to solve matrix equationsare compared through the theoretic estimation and numerical analysis. The merits aswell as demerits are presented and corresponding conclusions are obtained. Lastly, thespatial mixed discretization of TDMFIE is used for improving the computational precision of the algorithm. And the reason why the spatial mixed discretization ofTDMFIE can improve the computational precision is also given by theoretic analysis.Thirdly, the late-time instability of TDIE-based MOT scheme is intensively studied.At first, the sufficient stability condition of TDMFIE-based MOT scheme is obtainedthrough theoretical derivation using the norm. Utlizing the condition, the late-timestability of TDMFIE-based MOT scheme can be estimated effectively. Meanwhile, thesufficient and necessary stability condition is also deduced and acquired. Based on thecondition, an improved algorithm is proposed to improve the late-time instability andcomputational precision of TDMFIE-based MOT scheme. Then, the sufficient andnecessary stability condition of TDEFIE-based MOT scheme is derived and obtainedtheoretically. A method to analyze the results in late-time of TDEFIE-based MOTscheme is also proposed. Using this method, in the case of only changing the incidentwave, the transient currents in late-time can be calculated much faster. Finally, thesufficient and necessary stability condition of TDCFIE-based MOT scheme is gotaccording to theoretical derivation. The stability condition is validated by numericalresults. And the stability comparisons of TDCFIE with TDEFIE and TDMFIE are alsogiven by numerical results.At last, two-level PWTD algorithm is proposed to improve the efficiency ofTDIE-based MOT scheme. The fundamental of two-level PWTD algorithm is analyzedtheoretically. Using the plane wave expansions and choosing appropriate duration ofsub-signals can achieve fast computation of time-domain electromagnetic scatteringfields. The numerical techniques of two-level PWTD algorithm, containing scattererspatial partition, source signal segmentation and fitting, numerical computation of thetransmission function and the integral of spatial spectrum are mainly analyzed.Meanwhile, the main factors affecting the compututational precision of two-levelPWTD algorithm are also analyzed. In the final part, the optimums of the importantparameters in the algorithm are discussed by theoretical analysis and numerical results.The computational complexity of two-level PWTD algorithm is contrasted by that ofthe traditional MOT scheme.