Abstract
In this paper, a set of closed-form formulas for vector Finite Element Method (FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme. By analyzing the open region problems, the first-order Absorbing Boundary Condition (ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form. Based on the formulas, the hybrid Expanded Cholesky Method (ECM) and MultiFrontal algorithm (MF) is applied to solve finite element equations. Using the closed-form solution, the electromagnetic field of three dimensional targets can be studied sententiously and accurately. Simulation results show that the presented formulas are successfully and concise, which can be easily used to analyze three dimensional electromagnetic problems.
Similar content being viewed by others
References
J. M. Jin and D. J. Riley. Finite Element Analysis of Antennas and Arrays. Hoboken, New Jersey, John Wiley & Sons, Inc., 2008, 17–23.
E. A. Dunn, J. K. Byun, E. D. Branch, et al. Numerical simulation of BOR scattering and radiation using a higher order FEM. IEEE Transactions on Antennas and Propagation, 54(2006)3, 945–952.
J. Liu and J. Jin. Scattering analysis of a large body with deep cavities. IEEE Transactions on Antennas and Propagation, 51(2003)6, 1157–1167.
D. Arena, M. Ludovico, G. Manara, et al. Analysis of waveguide discontinuities using edge elements in a hybrid mode matching/finite elements approach. IEEE Microwave and Wireless Components Letters, 11(2001)9, 379–381.
J. L. Volakis, A. Chatteriee, and L. C. Kempel. Finite element method for electromagnetics: antennas, microwave circuits, and scattering applications. New York, US, Institute of Electrical and Electronics Engineers, Inc., 1998, 137–145.
J. M. Jin. The Finite Element Method in Electromagnetics. New York, US, John Wiley & Sons, Inc., 2002, 273–328.
C. Zuffada, T. Cwik, and V. Jamnejad. Modeling radiation with an efficient hybrid finite-element integral-equation waveguide mode-matching technique. IEEE Transactions on Antennas and Propagation, 45(1997)1, 34–39.
A. Chatterjee, J. M. Jin, and J. L. Volakis. Edge-based finite elements and vector ABCs applied to 3-D scattering. IEEE Transactions on Antennas and Propagation, 41(1993)2, 221–226.
J. M. Jin, J. L. Volakis and J. D. Collins. A finite element-boundary integral method for scattering and radiation by two-and three-dimensional structures. IEEE Transactions on Antennas and Propagation, 33(1991)3, 22–32.
J. K. Reid and J. A. Scott. An out-of-core sparse Cholesky solver. ACM Transactions on Mathematical Software (TOMS), 36(2009)2, 1–33.
R. S. Chen, D. X. Wang, E. K Yung, et al. Application of the multifrontal method to the vector FEM for analysis of microwave filters. Microwave and Optical Technology Letters, 31(2001)6, 465–470.
J. W. Liu. The multifrontal method for sparse matrix solution: Theory and practice. Society for Industrial and Applied Mathematics, 34(1992)1, 82–109.
J. Tian, Z. Q. Lv, X. W. Shi, et al. An efficient approach for multifrontal algorithm to solve non-positive-definite finite element equations in electromagnetic problems. Progress in Electromagnetics Research, 95(2009), 121–133.
A. Chatterjee, J. M. Jin, and J. L. Volakis. Computation of cavity resonances using edge-based finite elements. IEEE Transactions on Antennas and Propagation, 40(1992)11, 2106–2108.
J. M. Jin and J. L. Volakis. A biconjugate gradient FFT solution for scattering by planar plates. Electromagnetics, 12(1992)1, 105–119.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Science Foundation of China (No. 60801039).
Communication author: Tian Jin, born in 1982, female, Ph.D. candidate.
About this article
Cite this article
Tian, J., Gong, L., Shi, X. et al. The closed-form solution of vector finite element integral equations for three dimensional electromagnetic analysis. J. Electron.(China) 28, 602–608 (2011). https://doi.org/10.1007/s11767-012-0713-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11767-012-0713-2
Key words
- Vector Finite Element Method (FEM)
- Absorbing Boundary Condition (ABC)
- Expanded Cholesky Method (ECM)
- MultiFrontal algorithm (MF)