グラフ構造に基づく B-spline 重合メッシュ法の領域分割型並列解析

抄録

S-version of finite element method (SFEM) has intrinsic advantages of local high accuracy, low computation time, and simple meshing procedure, because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial resolutions. However, the conventional SFEM has disadvantages such as accuracy of numerical integration and matrix singularity. Thus, we have proposed a new framework, B-spline SFEM (BSFEM), which solves their problems, and improves the accuracy and the convergence of matrix calculations. On the other hand, to analyze larger problems, parallel programming with message passing interface (MPI) is necessary, assuming the use of distributed memory parallel computers. However, there are few studies on parallelization of SFEM, especially applying domain decomposition methods commonly used in finite element methods due to the complexity of its mesh structure. In this study, parallel computing of BSFEM is realized by generalizing the complex mesh structure into a graph that represents the interaction between computation nodes. To evaluate its parallel performance, we performed strong scaling tests.