Robust and efficient evaluation of functionals on parametric surfaces

Abstract

A robust and efficient algorithm for the numerical evaluation of functionals on surfaces is presented. The efficiency of the algorithm results from the adaption of powerful quadrature techniques to a particular geometric setting. It is obtained through a modification of the Romberg-quadrature which does not require subdivisions on the domain uniformly, but allows the use of a selective refinement strategy. The robustness of the algorithm is due to the exact arithmetic operations that sums up intermediate results without errors. This exact arithmetic does not affect the performance of the algorithm but it prevents the quadrature algorithm from accumulating rounding errors.