Two multipole alternatives based on Taylor series expansions for 3D BEM elasticity formulation

It has been previously reported in the open literature that multipole boundary element strategy based on Taylor expansions can result in computer codes which require O(NlogN) operations for problems with N degrees of freedom. Recently, Popov and Power [1] presented a multipole BEM strategy developed for 3D elasticity problems which is based on Taylor expansions but requires only O(N) operations and O(N) memory. Popov and Power's efficient algorithm results from the use of a clustering technique, first shift, in combination with an additional Taylor series expansion around the collocation points, second shift. In this work we present a comparison between two algorithms where the first or first and second clustering shifts are employed for 3D elasticity problems, addressing the advantages and disadvantages of each of the approaches.