A dynamic algorithm for integration in the boundary element method

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Department of Mechanical Engineering-Engineering Mechanics


The discretization of the boundary in boundary element method generates integrals over elements that can be evaluated using numerical quadrature that approximate the integrands or semi-analytical schemes that approximate the integration path. In semi-analytical integration schemes, the integration path is usually created using straight-line segments. Corners formed by the straight-line segments do not affect the accuracy in the interior significantly, but as the field point approaches these corners large errors may be introduced in the integration. In this paper, the boundary is described by a cubic spline on which an integration path of straight-line segments is dynamically created when the field point approaches the boundary. The algorithm described improves the accuracy in semi-analytical integration schemes by orders of magnitude at insignificant increase in the total solution time by the boundary element method. Results from two indirect BEM and a direct BEM formulation in which the unknowns are approximated by linear and quadratic Lagrange polynomial and a cubic Hermite polynomial demonstrate the versatility of the described algorithm.

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© 1998 John Wiley & Sons, Ltd. Publisher’s version of record: https://doi.org/10.1002/(SICI)1097-0207(19980228)41:4<639::AID-NME303>3.0.CO;2-6

Publication Title

International Journal for Numerical Methods in Engineering