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The method of moments (MoM), also known as the moment method and method of weighted residuals, is a numerical method in computational electromagnetics. It is used in computer programs that simulate the interaction of electromagnetic fields such as radio waves with matter, for example antenna simulation programs like NEC that calculate the radiation pattern of an antenna. Generally being a frequency-domain method, it involves the projection of an integral equation into a system of linear equations by the application of appropriate boundary conditions. This is done by using discrete meshes as in finite difference and finite element methods, often for the surface. The solutions are represented with the linear combination of pre-defined basis functions; generally, the coefficients of these basis functions are the sought unknowns. Green's functions and Galerkin method play a central role in the method of moments.
References
- ↑ J.W. Bandler, R.M. Biernacki, S.H. Chen, P.A. Grobelny, and R.H. Hemmers, “Space mapping technique for electromagnetic optimization,” IEEE Trans. Microwave Theory Tech., vol. 42, no. 12, pp. 2536–2544, Dec. 1994.
- ↑ J.W. Bandler, R.M. Biernacki, S.H. Chen, R.H. Hemmers, and K. Madsen, “Electromagnetic optimization exploiting aggressive space mapping,” IEEE Trans. Microwave Theory Tech., vol. 43, no. 12, pp. 2874–2882, Dec. 1995.
- ↑ A.J. Booker, J.E. Dennis, Jr., P.D. Frank, D.B. Serafini, V. Torczon, and M.W. Trosset,"A rigorous framework for optimization of expensive functions by surrogates," Structural Optimization, vol. 17, no. 1, pp. 1–13, Feb. 1999.
- ↑ J.W. Bandler, Q. Cheng, S.A. Dakroury, A.S. Mohamed, M.H. Bakr, K. Madsen and J. Søndergaard, "Space mapping: the state of the art," IEEE Trans. Microwave Theory Tech., vol. 52, no. 1, pp. 337–361, Jan. 2004.
- ↑ T.D. Robinson, M.S. Eldred, K.E. Willcox, and R. Haimes, "Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping," AIAA Journal, vol. 46, no. 11, November 2008.
- ↑ M. Redhe and L. Nilsson, “Optimization of the new Saab 9–3 exposed to impact load using a space mapping technique,” Structural and Multidisciplinary Optimization, vol. 27, no. 5, pp. 411–420, July 2004.
- ↑ J.E. Rayas-Sanchez, "Power in simplicity with ASM: tracing the aggressive space mapping algorithm over two decades of development and engineering applications", IEEE Microwave Magazine, vol. 17, no. 4, pp. 64–76, April 2016.
- ↑ J.W. Bandler and S. Koziel "Advances in electromagnetics-based design optimization", IEEE MTT-S Int. Microwave Symp. Digest (San Francisco, CA, 2016).
- Jan Mandel and Bedrich Sousedik, "Coarse space over the ages", Nineteenth International Conference on Domain Decomposition, Springer-Verlag, submitted, 2009. arXiv:0911.5725
- Olof B. Widlund, "The Development of Coarse Spaces for Domain Decomposition Algorithms", in: Domain Decomposition Methods in Science and Engineering XVIII, Bercovier, M. and Gander, M.J. and Kornhuber, R. and Widlund, O. (eds.), Lecture Notes in Computational Science and Engineering 70, Springer-Verlag, 2009, Proceedings of 18th International Conference on Domain Decomposition, Jerusalem, Israel, January 2008, doi : 10.1007/978-3-642-02677-5_26.