有限要素解析の低次元化モデル構築におけるhyper-reductionの並列化

抄録

In the field of structural analysis using the finite element method (FEM), the demand for detailed analysis is increasing, and techniques for large scale analysis have become an important factor. Distributed memory parallel computing is the key method that mitigates the effects of memory usage by distributing tasks and memories to multiple computation nodes. However, the performance of computers is limited, and the degree of freedom that can be handled depends on each environment. Thus, it is important to develop the method that can save the memory usage. Parametric studies are used in manufacturing to optimize designs, but it is impractical to cover every parameter combination. Therefore, projection based reduced order models (ROM) come into focus. However, the cost of projection operations is the bottleneck for ROM analysis. To solve this issue, empirical cubature method, which is one of the hyper-reduction methods, save the memory usage by the efficient integration performed by sparse element-wise weighting. This element-wise weights are obtained by sparse non-negative least squares method (sparse NNLS). In this study, we suggest the sparse NNLS algorithm corresponding the distributed memory parallel computing and evaluate the impact on the memory usage, the computation time, and the accuracy.