Abstract
In this paper the algebraic multi-grid principle is applied to the multilevel moment method, which makes the new multilevel method easier to implement and more adaptive to structure. Moreover, the error spectrum is analyzed, and the reason why conjugate gradient iteration is not a good relaxation scheme for multi-grid algorithm is explored. The numerical results show that our algebraic block Gauss Seidel multi-grid algorithm is very effective.
Similar content being viewed by others
References
R. F. Harington, Field Computation by Moment Methods. New York: Macmillan, 1968.
V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions, J. Comput. Phys., 86(1990)2, 414–439.
R. Coifman, V. Roklin, S. Wandzura, The fast multipole method for the wave equation: A pedestrian prescription, IEEE Antennas Propagat. Mag., 35(1993)3, 7–12.
A. Brandt, Multi-level adaptive solutions to boundary value problems, Math. Comput., 31(1977)2, 330–390.
K. Kalbasi, K. R. Demarest, A multilevel formulation of the method of moments, IEEE Trans. on Antennas and Propagation, AP-41(1993)5, 589–598.
S. Costiner, Multilevel methods applied to the design of resonant cavities, IEEE Trans. on Microwave Theory Tech., MTT-43(1995)1, 48–55.
C. Wei, N. Inagaki, W. Di, Dimension-descent technique for electromagnetic problem, IEE Proc.-H., 144(1997)5, 372–376.
A. Brandt, Algebraic multi-grid theory: the symmetric case, Applied Mathematics and Computation, 19(1986)1, 23–56.
C. F. Wang, D.G. Fang, Application of multi-grid method to computation of EM scattering problems, J. Systems Engineering and Electronics, 8(1997)2, 22–25.
J. Xu, Theory of multilevel methods, PhD thesis, USA: Cornell University, 1989.
A. Brant, S. Taasan, Multgrid methods for nearly singular and slightly indefinite problem, in Lecture Notes in Mathematics, No. 1228, W. Hackbuch and U. Trottenberg, Eds. Berlin: Springer-Verlag, 1986.
Author information
Authors and Affiliations
Additional information
Supported by the National Natural Science Foundation of China
About this article
Cite this article
Xu, Y., Fang, D. Algebraic multi-grid method in two-dimension electrically large problems. J. of Electron.(China) 17, 77–83 (2000). https://doi.org/10.1007/s11767-000-0025-9
Issue Date:
DOI: https://doi.org/10.1007/s11767-000-0025-9