结构非匹配网格区域分裂的并行数值计算研究

Study on Parallel Numerical Calculation of Structural Domain Decomposition with Non-Matching Meshes

针对非匹配多域结构有限元问题的并行求解,在L-FETI算法基础上,通过引入框架节点力及修改框架位移协调条件和载荷平衡条件,推导出了非匹配有限元撕裂合并并行算法。基于RBF插值技术,在非匹配界面上引入局部坐标系,使相邻子域间内力和位移的数据传递具有统一的矩阵格式,更易于编程。以四区域板弯有限元模型为例,分别构建匹配网格与非匹配网格两种分区模型,数值结果显示分区框架上相同节点的挠度位移具有很好的吻合度,表明提出的方法在非匹配多子域的并行求解中合理有效。

For the parallel solution of structural finite element problem with non-matching multi-domains, a nonmatched finite element tearing and interconnectiong(FETI) parallel algorithm is proposed based on L-FETI method by introducing the frame node force and modifying the frame displacement compatibility condition and the load balance condition. Based on the radial basis functions(RBF) interpolation technique, the data transfer of internal force and displacement between the neighboring subdomains has a unified matrix format and is easy to program by introducing a local coordinate system into the non-matching interfaces. Taking the finite element model for plate bending problem with four subdomains as an example, two kinds of multi-domains models, matching and non-matching meshes, are constructed respectively. The numerical results show that the out-of-plane deflection of the same nodes on the domain decomposition frame is in a good agreement, which shows that the present method is reasonable and effective for solving the parallel non-matching multi-domains model.