微分求积区域分裂法在裂缝问题上的应用

Application of differential quarature domain decomposition method to the problem with crack

微分求积法DQM在处理裂缝问题时,会产生很大的误差。因此,本文用微分求积法结合不带重叠的区域分裂法DQDDM来求解。通过本文的讨论,可以看到DQDDM在处理裂缝问题时,在节点数目不多的条件下获得比较精确的解,同时计算量又不大。

In this paper, a new method DQDDM （Differential Quadrature Domain Decomposition Method） is presented. We divide the computational domain into several non-overlapping subdomains, and DQM is applied in each subdomains respectively. Numerical boundary reduction technique independent of the basic solution of the differential equation is used. By eliminating the interior points and combining with the block matrix technique, the differential equation is reduced to linear algebraic equations which include the boundary points only. The complexity of the computation is reduced greatly. The numerical results are satisfactory.