Geodesic
Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D
Applications of Mathematics, Tome 59 (2014) no. 5, pp. 527-542.

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We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations on these results.
DOI : 10.1007/s10492-014-0070-6
Classification : 65N38
Keywords: boundary element method; Galerkin discretization; Helmholtz equation; hypersingular boundary integral equation 
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Zapletal, Jan; Bouchala, Jiří. Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D. Applications of Mathematics, Tome 59 (2014) no. 5, pp. 527-542. doi : 10.1007/s10492-014-0070-6. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0070-6/

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