Minimizing The 3D Solenoidal Basis Set in Method of Moments Based Volume Integral Equation

Authors

  • A. Obi GE Global Research, Niskayuna, NY12309, USA
  • R. Lemdiasov PhiHealth, Richardson, TX75075, USA
  • R. Ludwig Worcester Polytechnic Institute, Worcester, MA01609, USA Department of Electrical and Computer Engineering

Keywords:

Divergence-free, method of moments (MoM), solenoidal edge basis function

Abstract

A method for completely minimizing a 3D-solenoidal basis set, and identifying its linearly independent basis functions in method of moments (MoM) based volume integral equation (VIE) is presented. The method uses the connecting information of the geometric mesh and the properties of the 3D solenoidal basis function to remove the null space of the basis set. Consequently, the approach is not prone to numerical inaccuracies due to finite machine precision resulting from matrix manipulations. In addition, our method is not restricted to simply connected or contiguous mesh regions; it is applicable to a wide variety of complicated mesh regions featuring holes and voids. Finally, an expression for determining the minimum number of linearly independent solenoidal basis functions in a given tetrahedral mesh is presented.

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References

D. Schaubert, D. Wilton, and A. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrary shaped inhomogeneous dielectric bodies,” )%%% 4RANS !NTENNAS 0ROPAGAT., vol. 32, no. 1, pp. 77-85, Jan. 1984.

S. Kulkani, R. Lemdiasov, R. Ludwig, and S. Makarov, “Comparison of two sets of low-order basis functions for tetrahedral VIE modeling,” )%%% 4RANS !NTENNAS 0ROPAGAT, vol. 52, no. 10, pp. 2789-2795, Oct. 2004.

R. Lemdiasov and R. Ludwig, “The determination of linearly independent rotational basis functions in volumetric electric field integral equations,” )%%% 4RANS !NTENNAS 0ROPAGAT, vol. 54, no. 7, pp. 2166-2169, July 2006.

J. Ding, R. Chen, J. Zhu, Z. Fan, and D. Ding, “A redundant loop basis for closed structures with application to MR basis,” !#%3*OURNAL , vol. 26, no. 3, March 2011.

M. Li and W. Chew, “Applying divergence-free condition in solving the volume integral equation,” 0ROGR)N%LECTR2ESEARCH, PIER 57, pp. 311-333, 2006.

B. Rubin, “Divergence-free basis for representing polarization current in finite-size dielectric regions,” )%%%4RANS!NTENNAS0ROPAGAT., vol. 41, no. 3, pp. 269-277, March 1993.

S. Carvalho and L. Mendes, “Method of moments with solenoidal basis functions: An approach to analyze the scattering by inhomogeneous dielectrics,” IN #OMPU %LECTRO #ONF., no. 420, April, 1996.

S. Carvalho and L. Mendes, “Scattering of EM waves by inhomogeneous dielectric with the use of the method of moments and 3-D solenoidal basis functions,” -ICROW/PT4ECHN,ETT, vol. 23, no. 1, pp. 42-46, 1999.

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Published

2021-09-27

How to Cite

[1]
A. . Obi, R. . Lemdiasov, and R. . Ludwig, “Minimizing The 3D Solenoidal Basis Set in Method of Moments Based Volume Integral Equation”, ACES Journal, vol. 28, no. 10, pp. 903–908, Sep. 2021.

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General Submission