Reusable intrinsic sample point (RISP) algorithm for the efficient numerical integration of three dimensional curved boundary elements

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Abstract
This paper presents an algorithm that provides an order of magnitude gain in the computational performance of the numerical integration of the boundary integral equations for three dimensional analysis. Existing algorithms for numerical integration have strategically clustered integration sample points based on the relative proximity of the load points to the boundary element being integrated using element subdivision or element co‐ordinate transformation. The emphasis in these techniques has been on minimizing the number of sample points required to obtain a given level of accuracy. The present algorithm, while closely following the spirit of these earlier approaches, employs a discrete number of sets of predetermined, customized, near‐optimum, sample point quantities associated with the intrinsic boundary element. The ability created by this approach to reuse sample point geometric information of the actual element allows for the realization of substantive computational economy. This algorithm provides accurate and efficient numerical results both when load points are far from, and when they are on the boundary element being integrated. Numerical results are provided to demonstrate the substantial economy achieved through the use of the present algorithm.

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