The vectorization expressions of Taylor series multipole-BEM for 3D elasticity problems

摘要

The Taylor Series Multipole Boundary Element Method (TSMBEM) can improve the computational efficiency of Boundary Element Methods (BEM) efficiently, which only requires O(N) computational costs (operations and memory) for a problem with N unknowns. But the Taylor expansions of fundamental solutions are generally expressed using tensor form in the literatures about TSMBEM. Although these kinds of formulations are easy to program, many repetitious operations are executed and many equivalent terms are saved, it will result in the waste of memory. It is presented that the vectorization expressions of Taylor series multipole boundary element formula for elasticity problems, which take account of the symmetric properties of fundamental solutions and the characteristic of 3D components. The vectorization formulations reduce the computational operations and storage required, and improve the computational efficiency. The validity and efficiency of proposed scheme are demonstrated by the numerical experiments.