Boundary Integral Evaluation of Surface Derivatives

In boundary element analysis, first order function derivatives, e.g., boundary potential gradient or stress tensor, can be accurately computed by evaluating the hypersingular integral equation for these quantities. However, this approach requires a complete integration over the boundary and is therefore computationally quite expensive. Herein it is shown that this method can be significantly simplified: only local singular integrals need to be evaluated. The procedure is based upon defining the singular integrals as a limit to the boundary and exploiting the ability to use both interior and exterior boundary limits. Test calculations for two- and three-dimensional problems demonstrate the accuracy of the method.

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