CAJ | 학술논문

提出一种基于多极边界元法(FM-BEM)的规划-迭代型不完全广义极小残值法(简称IGMRES(m)),并建立其收敛性理论.新求解算法采用截断技术,在迭代时仅使用前面计算出的部分向量构造新的递推式以计算后面的向量,矩阵和向量的乘积采用多极展开法(FMM)计算,使得计算量和存储量大为减少.通过数值试验证明,新算法可有效地处理弹塑性摩擦接触迭代的繁杂和费时问题,在确保数值计算精度的前提下,可大大减少迭代次数,显著提高计算效率.
제출일충기우다겁변계원법(FM-BEM)적규화-질대형불완전엄의겁소잔치법(간칭IGMRES(m)),병건립기수렴성이론.신구해산법채용절단기술,재질대시부사용전면계산출적부분향량구조신적체추식이계산후면적향량,구진화향량적승적채용다겁전개법(FMM)계산,사득계산량화존저량대위감소.통과수치시험증명,신산법가유효지처리탄소성마찰접촉질대적번잡화비시문제,재학보수치계산정도적전제하,가대대감소질대차수,현저제고계산효솔.
A new program-iteration pattern algorithm, incomplete generalized minimal residual method (IGMRES(m)) based on the fast multipole boundary element method (FM-BEM), was proposed for the solution of highly nonlinear equations and its convergence theory was established. With help of truncation technology, a new recursion formulae with the proposed method using only some of the calculated vectors to compute the following vectors, which could greatly reduce the computation and memory requirement. The fast multipole method (FMM) was used to compute the matrix-vector products. Numerical experiments proved that the new algorithm is highly efficient for computing elasto-plastic frictional contact problems, especially for complicated iteration and time-consuming calculation. And it can greatly reduce the iteration times and improve computational efficiency with ensured numerical accuracy.