Error analysis and novel near-field preconditioning techniques for Taylor series multipole-BEM

The Taylor series multipole boundary element method (TSMBEM) improves the efficiency of boundary element method (BEM) by reducing the required operations and computer memory. However, the precision of TSMBEM is sacrificed comparing to the conventional BEMs. To quantify the accuracy of TSMBEM in solving 3D elasticity problems, error analysis is performed. A novel near-field preconditioning technique is presented for fast multipole-BEM based on the degressive regularity of fundamental solutions. The correctness and effectiveness of error estimate formula and near-field preconditioning technique is demonstrated by numerical examples.