We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is intro...We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.展开更多
A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing ...A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.展开更多
Based on the dipole source method, all components of the Green＇s functions in spectral domain are restructured concisely by four basis functions, and in terms of the two-level discrete complex image method （DCIM） w...Based on the dipole source method, all components of the Green＇s functions in spectral domain are restructured concisely by four basis functions, and in terms of the two-level discrete complex image method （DCIM） with the high order Sommerfeld identities, an efficient algorithm for closed-form Green＇s functions in spatial domain in multilayered media is presented. This new work enjoys the advantages of the surface wave pole extraction directly carried out by the generalized integral path without troubles of that all components of Green＇s function in spectral domain should be reformed respectively in transmission line network analogy, and then the Green＇s functions for mixed-potential integral equation （MPIE） analysis in both near-field and far-field in multilayered media are obtained. In addition, the curl operator for coupled field in MPIE is avoided conveniently. It is especially applicable and useful to characterize the electromagnetic scattering by, and radiation in the presence of, the electrically large 3-D objects in multilayered media. The numerical results of the S-parameters of a microstrip periodic bandgap （PBG） filter, the radar cross section （RCS） of a large microstrip antenna array, the characteristics of scattering, and radiation from the three-dimensional （3-D） targets in multilayered media are obtained, to demonstrate better effectiveness and accuracy of this technique.展开更多
The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms o...The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green＇s function in real space. The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost. Subsequently, a fast integral equation solver with O（N2zNxNy log（NzNy）） in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the n-th order Bessel function in 2-D. Computational cost and parallel efficiency of the new algorithm are presented.展开更多
This dissertation deals with the internal waves generated by a submergedmoving body in stratified fluids by combining theoretical and experimental methods. Our purpose isto provide some scientific evidences for non-ac...This dissertation deals with the internal waves generated by a submergedmoving body in stratified fluids by combining theoretical and experimental methods. Our purpose isto provide some scientific evidences for non-acoustic detection of underwater moving bodies based onthe principles of dynamics of the internal waves. An approach to velocity potentials obtained bysuperposing Green''s functions of sources and sinks was proposed for Kelvin waves at the free surfaceor interface in a two-layer fluid. The effects of interacting surface- and internal-wave modesinduced by a dipole on the surface divergence field were investigated. A new theoretical modelformulating the interaction of a two-dimensional submerged moving body with the conjugate flow in athree-layer fluid was established. An exact solution satisfying the two-dimensional Benjamin-Onoequation was obtained and the vertically propagating properties of the weakly nonlinear long waveswere studied by means of the ray theory and WKB method. The above theoretical results arequalitatively consistent with those obtained in the experiments conducted by the author.展开更多
基金supported by CNSF(Granted No.40874050)Chinese High Technology Project(Granted No.2011YQ05006010)
文摘We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.
文摘A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.
基金the National Natural Science Foundation of China (Grant No. 60371020)National Defense Pre-research Foundation of China (Grant No. 9140a03020206dz0112)
文摘Based on the dipole source method, all components of the Green＇s functions in spectral domain are restructured concisely by four basis functions, and in terms of the two-level discrete complex image method （DCIM） with the high order Sommerfeld identities, an efficient algorithm for closed-form Green＇s functions in spatial domain in multilayered media is presented. This new work enjoys the advantages of the surface wave pole extraction directly carried out by the generalized integral path without troubles of that all components of Green＇s function in spectral domain should be reformed respectively in transmission line network analogy, and then the Green＇s functions for mixed-potential integral equation （MPIE） analysis in both near-field and far-field in multilayered media are obtained. In addition, the curl operator for coupled field in MPIE is avoided conveniently. It is especially applicable and useful to characterize the electromagnetic scattering by, and radiation in the presence of, the electrically large 3-D objects in multilayered media. The numerical results of the S-parameters of a microstrip periodic bandgap （PBG） filter, the radar cross section （RCS） of a large microstrip antenna array, the characteristics of scattering, and radiation from the three-dimensional （3-D） targets in multilayered media are obtained, to demonstrate better effectiveness and accuracy of this technique.
基金supported by the US Army Ofce of Research(Grant No.W911NF11-1-0364)the National Science Foundation of USA(Grant No.DMS-1005441)National Natural Science Foundation of China(Grant No.91230105)
文摘The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green＇s function in real space. The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost. Subsequently, a fast integral equation solver with O（N2zNxNy log（NzNy）） in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the n-th order Bessel function in 2-D. Computational cost and parallel efficiency of the new algorithm are presented.
文摘This dissertation deals with the internal waves generated by a submergedmoving body in stratified fluids by combining theoretical and experimental methods. Our purpose isto provide some scientific evidences for non-acoustic detection of underwater moving bodies based onthe principles of dynamics of the internal waves. An approach to velocity potentials obtained bysuperposing Green''s functions of sources and sinks was proposed for Kelvin waves at the free surfaceor interface in a two-layer fluid. The effects of interacting surface- and internal-wave modesinduced by a dipole on the surface divergence field were investigated. A new theoretical modelformulating the interaction of a two-dimensional submerged moving body with the conjugate flow in athree-layer fluid was established. An exact solution satisfying the two-dimensional Benjamin-Onoequation was obtained and the vertically propagating properties of the weakly nonlinear long waveswere studied by means of the ray theory and WKB method. The above theoretical results arequalitatively consistent with those obtained in the experiments conducted by the author.
