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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2015-08-12
A Method to Calculate the Spherical Multipole Expansion of the Electrostatic Charge Distribution on a Triangular Boundary Element
By
John Barrett,

    Mr. John Barrett

    Physics

    Massachusetts Institute of Technology

    USA

    Homepage

Joseph A. Formaggio,

    Prof. Joseph A. Formaggio

    Institute of Technology

    USA

    Homepage

Thomas Joseph Corona

    Dr. Thomas Joseph Corona

    Physics Department

    University of North Carolina at Chapel Hill

    USA

    Homepage

Progress In Electromagnetics Research B, Vol. 63, 123-143, 2015
doi:10.2528/PIERB15061904 | Google Scholar

Abstract
We describe a technique to analytically compute the multipole moments of a charge distribution confined to a planar triangle, which may be useful in solving the Laplace equation using the fast multipole boundary element method (FMBEM) and for charged particle tracking. This algorithm proceeds by performing the necessary integration recursively within a specific coordinate system, and then transforming the moments into the global coordinate system through the application of rotation and translation operators. This method has been implemented and found use in conjunction with a simple piecewise constant collocation scheme, but is generalizable to non-uniform charge densities. When applied to low aspect ratio (≤100) triangles and expansions with degree up to 32, it is accurate and efficient compared to simple two-dimensional Gauss-Legendre quadrature.
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Citation
John Barrett, Joseph A. Formaggio, and Thomas Joseph Corona, "A Method to Calculate the Spherical Multipole Expansion of the Electrostatic Charge Distribution on a Triangular Boundary Element," Progress In Electromagnetics Research B, Vol. 63, 123-143, 2015.
doi:10.2528/PIERB15061904
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