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PIER PIER B PIER C PIER M PIER Letters
2011-06-10
On the Analytic-Numeric Treatment of Weakly Singular Integrals on Arbitrary Polygonal Domains
By
Sergio Lopez-Pena,

    Dr. Sergio Lopez-Pena

    EPFL STI ITOP LEMA

    Switzerland

    Homepage

Athanasios G. Polimeridis,

    Dr. Athanasios G. Polimeridis

    STI

    EPFL

    Switzerland

    Homepage

Juan Mosig

    Dr. Juan Mosig

    Chairman of EPFL SpaceCenter

    Ecole Polytechnique Fédérale de Lausanne (EPFL)

    Switzerland

    Homepage

Progress In Electromagnetics Research, Vol. 117, 339-355, 2011
doi:10.2528/PIER11050504
Abstract
An alternative analytical approach to calculate the weakly singular free-space static potential integral associated to uniform sources is presented. Arbitrary oriented flat polygons are considered as integration domains. The technique stands out by its mathematical simplicity and it is based on a novel integral transformation. The presented formula is equivalent to others existing in literature, being also concise and suitable within a singularity subtraction framework. Generalized Cartesian product rules built on the double exponential formula are utilized to integrate numerically the resulting analytical 2D potential integral. As a consequence, drawbacks associated to endpoint singularities in the derivative of the potential are tempered. Numerical examples within a surface integral equation-Method of Moments framework are finally provided.
Citation
Sergio Lopez-Pena, Athanasios G. Polimeridis, and Juan Mosig, "On the Analytic-Numeric Treatment of Weakly Singular Integrals on Arbitrary Polygonal Domains," Progress In Electromagnetics Research, Vol. 117, 339-355, 2011.
doi:10.2528/PIER11050504
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