A. Salvadori

Analytical integrations in 3D BEM

Pages 27-68
Received: 2 March 2008
Mathematics Subject Classification (2000): 65R20
Keywords: Integral equations, boundary elements, analytical integrations, finite part of Hadamard.

Abstract Some results on the analytical integration of kernels in elliptic [1] problems (potential, Stokes, elasticity) for 3D Boundary Element Methods are presented for isotropic homogeneous materials. Adopting polynomial shape functions of arbitrary degree on flat triangular discretizations, integrations are performed for Lebesgue integrals working in a local coordinate system. For singular integrals, both a limit to the boundary as well as the finite part of Hadamard [2,3] approach have been pursued.