On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions

Araújo, António; Serranho, Pedro

http://hdl.handle.net/10400.2/8521

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Authors

Araújo, António

Serranho, Pedro

Abstract(s)

The method of fundamental solutions is broadly used in science and engineering to numerically solve the direct time-harmonic scattering problem. In 2D the choice of source points is usually made by considering an inner pseudo-boundary over which equidistant source points are placed. In 3D, however, this problem is much more challenging, since, in general, equidistant points over a closed surface do not exist. In this paper we discuss a method to obtain a quasi-equidistant point distribution over the unit sphere surface, giving rise to a Delaunay triangulation that might also be used for other boundary element methods. We give theoretical estimates for the expected distance between points and the expect area of each triangle. We illustrate the feasibility of the proposed method in terms of the comparison with the expected values for distance and area. We also provide numerical evidence that this point distribution leads to a good conditioning of the linear system associated with the direct scattering problem, being therefore an adequated choice of source points for the method of fundamental solutions.