中文摘要：

研究了Krylov子空间GMRES（m）算法的基本理论，提出一种基于FMM的Krylov子空间截断型IGMRES（m）新算法．给出三物体弹性摩擦接触算例，计算结果表明，所提出算法在保证计算精度的前提下，可以大大减少迭代次数，显著提高计算效率．

英文摘要：

The fundamental theory of the Generalized Minimal Residual （GMRES（m）） algorithm was studied in Krylov subspace. A new truncation-pattern Incomplete Generalized Minimal Residual （IGMRES（m）） algorithm was proposed in Krylov subspace based on the Fast Multipole Method（FMM）. A numerical example was presented for 3-D elastic frictional contact. Numerical results showed that the new algorithm could greatly reduce the iteration number and improve the computational efficiency with ensured numerical accuracy.