Application of the extended boundary condition method to particles with sharp edges: A comparison of two surface integration approaches

We discuss, test, and compare two surface integration approaches that have been proposed for applying the extended boundary condition method (EBCM) to particles with sharp edges. One is based on approximating surface parameterization by a smooth function. By investigating the accuracy of this approach we find a quantitative condition for the radius of curvature of the approximate particle surface at the edge. The second approach is based on a special quadrature scheme for performing surface integration in the EBCM. For the simple test case of a cubic particle we find that the numerical advantages of the second method outweigh those of the first method, resulting in an overall reduction of computation time by a factor of 2. We conclude that the second method is preferable to the first when one is dealing with regularly shaped particles, for which the special quadrature scheme is reasonably simple to implement, and with particles with a relatively small number of sharp edges.