三维弹性快速多极边界元法

Three-dimensional elastic fast multipole BEM

将静电场多极展开法和广义极小残值法结合于三维弹性问题的边界元法,使其求解的计算量及所需内存量同节点的自由度总数成正比,变革计算结构,加快求解速度以适应大规模数值计算。两者结合的关键点在于边界元法基本解的合理分解,并用广义极小残值法(GMRES)求解方程。轧机支承辊变形场大规模数值算例的总自由度数首次达N=34008并获得成功。清晰地描述了支承辊和工作辊接触区的辊型。

We incorporate fast multipole method and GMRES to Boundary Element Method, and use this method to solve the 3-D elastic problems. In this case, the memory and operations requiremented of a problem with N unknowns are proportional to N, and this method can speed up radically the computation and adapt to large scale numerical computing. The key of the method is mathematical decomposition of fundamental solutions of three-dimensional elasticity. And we use the generalized minimum residual algorithm (GMRES) to find the solution of matrix equation. By a large scale test, we get the balance point of the traditional BEM and the fast multipole BEM up to 1700-1800 degrees of freedom. The fast multipole BEM needs less memories than traditional BEM. This method is effective, and has extensive application prospect.