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Volume 22 Issue 6
Nov.  2000
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Chen Xiaoguang, Jin Yaqiu . THE FAST MULTIPOLE METHOD OF THREE DIMENSIONAL ELECTROMAGNETIC WAVE VOLUME INTEGRAL EQUATION(3DV-FMM)[J]. Journal of Electronics & Information Technology, 2000, 22(6): 1007-1015.
Citation: Chen Xiaoguang, Jin Yaqiu . THE FAST MULTIPOLE METHOD OF THREE DIMENSIONAL ELECTROMAGNETIC WAVE VOLUME INTEGRAL EQUATION(3DV-FMM)[J]. Journal of Electronics & Information Technology, 2000, 22(6): 1007-1015.

THE FAST MULTIPOLE METHOD OF THREE DIMENSIONAL ELECTROMAGNETIC WAVE VOLUME INTEGRAL EQUATION(3DV-FMM)

  • Received Date: 1998-12-31
  • Rev Recd Date: 1999-09-23
  • Publish Date: 2000-11-19
  • In this paper, a Fast Multipole Method (FMM) is developed to solving the scattered fields from three dimensional (3D) inhomogeneous dielectric scatterers. This generalized FMM is applied to the volume integral equation (3DV-FMM). The discrete formula of the volume integral equation was derived by the basic FMM and multi-level FMM. The FMM approach significantly reduces both the complexity of a matrix-vector multiplying and memory requirement. In calculation, the delta function is chosen as the basis and perfect convergence to the FMM results is achieved. As a typical example, the bistatic RCS of cubic scatterers with homogeneous, or inhomogeneous permittivity is calculated numerically. Distribution of electric currents on the cross-section of a dielectric cube is also obtained. Comparing with conventional moment method, the results of 3DV-FMM are exactly matched. However, the computer memory and CPU time are greatly reduced by using the 3DV-FMM. This method is applicable to the forward numerical simulation for 3D electromagnetic inverse problem.
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  • Engheta N, Murphy W D, Rokhlin V, et al. The fast multipole method (FMM) for electromagnetic scattering problems. IEEE Trans. on Antennas and Propagation, 1992, AP-40(6): 634-641.[2]Coifman R, Rokhlin V, Wandzura S. The fast multipole method for the wave equation: A pedestrian prescription. IEEE Antennas and Propagation Magazine, 1993, 35(3): 7-12.[3]Song J M, Chew W C. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering[J].Microwave Opt. Technol. Lett.1995, 10(1):14-19[4]Epton M A, Dembart B. Multipole translation theory for the there-dimensional Laplace and Helmholtz equations[J].SIAM J. Sci. Comput.1995, 16(4):865-897[5]Sheng X Q, Jin J M, Song J M,et al. On the formulation of hybrid finite-element and boundaryintegral method for 3-D scattering. IEEE Trans. on Antennas and Propagation, 1998, AP-46(3):303-311.[6]Zhao J S, Chew W C, Lu C C, et al. Thin-stratified medium fast-multipole algorithm for solving microstrip structures. IEEE Trans. on Microwave and Techniques Theory, 1998, MTT-46(4):395-403.[7]Song J M, Lu C C, Chew W C, et al. Fast Illinois solver code(FISC)[J].IEEE Antennas and Propagation Magazine.1998, 40(3):27-34[8]Wang J J H, Dubberley J R. Computation of fields in an arbitrarily shaped heterogeneous dielectric or biological body by an interative conjugate gradient method. IEEE Trans. on Microwave and Techniques Theory, 1989, MTT-37(7): 1119-1125.[9]Song J M, Lu C C, Chew W C. Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects. IEEE Trans. on Antennas and Propagation, 1997, AP-45(10): 1488-1493.
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