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.

Application of the extended boundary condition method to homogeneous particles with point-group symmetries.

The numerical evaluation of surface integrals is the most time-consuming part of the extended boundary condition method (EBCM) for calculating the T matrix. An efficient implementation of the method is presented for homogeneous particles with discrete geometric symmetries and is applied to regular polyhedral prisms of finite length. For such prisms, an efficient quadrature scheme for computing the surface integrals is developed. Exploitation of these symmetries in conjunction with the new quadrature scheme leads to a reduction in CPU time by 3 orders of magnitude from that of a general EBCM implementation with no geometry-specific adaptations. The improved quadrature scheme and the exploitation of symmetries account for, respectively, 1 and 2 orders of magnitude in the total reduction of the CPU time. Test results for scattering by rectangular parallelepipeds and hexagonal plates are shown to agree well with corresponding results obtained by use of the discrete-dipole approximation. A model application for various polyhedral prisms is presented.