Robust semi-analytical integration of singular impedance matrix elements in surface integral equation solvers
The direct evaluation method tailored to the 4-D singular integrals arising in the second-kind Fredholm surface integral equation formulations is presented. The proposed semi-analytical integration scheme extends the existing singularity cancellation methods, often used to tackle singular integrals, by utilizing a series of coordinate transformations combined with the re-ordering of the integrations. The overall algebraic manipulation results in a reduction of the dimensionality and the final 2-D kernels comprise sufficiently smooth behavior, allowing a straightforward treatment by standard quadrature rules. Numerical results demonstrate that one of the main error sources of the second-kind integral equations is undoubtedly cured.
2011
Istambul
978-1-4244-5117-3
REVIEWED
EPFL
Event name | Event place | Event date |
Istambul, Turkey | August 13-20, 2011 | |