Evaluation of Model Order Reduction using Empirical Cubature Method by Hierarchical Element Selection

In the Precise seismic analysis is essential for the safe structural design of nuclear reactors, but reducing its high computational cost is a practical challenge. This study investigates model order reduction using the POD-Galerkin method to address this issue. Due to the nonlinearity of seismic analysis, the repeated projection of the governing equations in the POD-Galerkin method becomes a computational bottleneck. Therefore, we employ a hyper-reduction technique, the Empirical Cubature Method (ECM), to approximate the projection and accelerate the computation. Both methods are data-driven, requiring an offline stage to compute the full-order model before the fast online stage. For large-scale problems like reactors, this offline stage must be executed in a domain-decomposed parallel environment. However, the offline process for ECM is based on a greedy algorithm, which is inherently serial and difficult to parallelize. Accordingly, this study proposes an approximate parallelization method for the ECM offline stage that can run in a domain-decomposed parallel environment. We will apply this method to a simplified model with geometric nonlinearity to evaluate its impact on computation time and accuracy.