Taylor series fast multipole boundary element method for solution of Reissner׳s shear deformable plate bending problems

In this paper, a new fast multipole BEM for the solution of Reissner׳s plates is presented. The suggested formulation is based on expressing the fundamental solutions in forms of potentials. Hence, these potentials and their relevant fundamental solutions are expanded by means of Taylor series expansions. Accordingly, the far field integrations are represented by these series expansions and summed for far clusters, whereas the near field integrations are kept to be computed directly. In the present formulation, equivalent collocations are based on both first and second shift collocations for kernels. By the present implementation of the fast multipole BEM in coupling with iterative solver (GMRES), the computational cost is rapidly reduced from O(N3) in the conventional BEM to O(N log N) and O(N) for first and second shift respectively. Numerical examples are given to demonstrate the efficiency of the formulation against the conventional direct BEM. The accuracy of the results is traced by truncating Taylor series expansions to certain terms. It was demonstrated via numerical examples that three terms for both first shift and second shift are enough to produce sufficient accuracy with substantial reduction of solution time.