A scheme to randomly generate surface dust points for the 3D complex variable boundary element method (CVBEM)

A scheme to randomly generate dust points on the surface of a three-dimensional (3D) object is proposed. This scheme will potentially eliminate the bias of a density of points which are approximately equally spaced on the surface, as well as eliminate possible weighting requirements for areas of higher density. This method has the potential to reduce computational effort, as fewer points might be required to define the surface area. The global trial function vector can be assigned to these dust points and then entered into the complex variable boundary element method (CVBEM) commercial code. This scheme can be applied to each piece of a system that is comprised of a connected multiple geometry. A noticeable benefit of this approach is that the same problem can be studied several times, using a new random distribution of surface points each time. The smallest error can then be determined and that run selected. The Mathematica code used to generate the scheme is attached as an appendix.