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On the efficient evaluation of hyper-singular integrals in Galerkin surface integral equation formulations via the direct evaluation method
Tamayo Palau, José María; Polimeridis, Athanasios G.; Rius Casals, Juan Manuel; Mosig, Juan Ramón
Universitat Politècnica de Catalunya. Departament de Teoria del Senyal i Comunicacions; Universitat Politècnica de Catalunya. ANTENNALAB - Grup d´Antenes i Sistemes Radio
In this paper, the direct evaluation method tailored for the hyper-singular integrals arising in Galerkin surface integral equation formulations is developed.[...] The proposed method utilizes a series of coordinate transformations together with a re-ordering of the integrations in order to reduce the 4-D hyper-singular integrals to 2-D smooth integrals that can be easily computed via generalized Cartesian product rules based on standard Gauss quadratures, readily available in the literature. The direct evaluation method was originally introduced by Gray et al. for the evaluation of super hyper-singular Galerkin surface integrals arising in static problems and recently it was extended for the case of the weakly singular integrals in Galerkin MoM problems over coincident triangle elements.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Galerkin methods
Integral equations
Matrices
Equacions integrals
Matrius (Matemàtica)
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