规划-迭代型弹塑性摩擦接触多极边界元法

提出基于多极展开法的规划-迭代型的高度非线性方程的IGMRES(m)高效求解法,并建立其收敛性理论。本法适用于三维弹塑性摩擦接触多极边界元法,有效处理弹塑性摩擦接触迭代的繁杂和费时问题。数值试验证明,本求解法在确保数值精度的前提下,可减少迭代次数,显著提高计算效率。

Program-iteration pattern Fast Multipole BEM for elasto-plastic contact with friction

A new program-iteration pattern method was proposed for the solution of highly nonlinear equations.It was named the Incomplete Generalized Minimal Residual Method(IGMRES(m)),which was based on the Fast Multipole Method(FMM).By using the truncation technology,the presented method constructed new recursion formulae only using some of the calculated vectors to compute theadvancing vectors,which could greatly reduce the computation and memory requirement.The FMM was used to compute the product of a matrix and some vectors.In combination with the Generalized Minimal Residual Method(GMRES(m)),the convergence theory of the IGMRES(m) was established.The presented method was well suitable for 3-D elasto-plastic frictional contact Fast Multipole Boundary Element Method(FM-BEM), which was much efficient for the elasto-plastic complicated iteration and timeconsuming problems.Numerical examples were given to prove that the new method could greatly reduce the iteration times and improve the computational efficiency with ensured numerical accuracy.