Comparison of reduced basis construction methods for Model Order Reduction, with application to non-linear low frequency electromagnetics

Numerical simulation is more and more used during the design stage of a manufactured product in order to optimize its performances. However, it is often too time consuming, particularly when it is used to solve optimization problems, preventing an intensive usage. A-posteriori Model Order Reduction methods can be very effective to shorten the computational time. An approximated solution is then sought in a space of small dimension defined by a reduced basis. The accuracy of such methods is highly dependent on the choice of the reduced basis, extracted from preliminary numerical simulation. The method usually applied to construct such reduced basis is based on the Singular Value Decomposition (SVD), which can be time consuming, and is not adapted when a large collection of preliminary numerical simulations must be used to construct the basis. An alternative to this approach has been proposed recently with the Maximum Entropy Snapshot Sampling (MESS) method. In this paper, we propose to compare these methods with other approaches usually used for clustering or data classification based on vectors distance calculation, like the Centroidal Voronoi Tessellation (CVT), Density Based Spatial Clustering of Applications with Noise (DBSCAN), and Clustering Using Representatives (CURE). The methods are compared on a complex and realistic nonlinear problem in low frequency electromagnetics. The quality of the reduced bases obtained by the different methods are compared. Then, field distributions and global quantities, like eddy current losses and magnetic energy, are computed from the reconstructed results, to further analyze the quality of the reduced bases. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

Numerical simulation is widely used for product design optimization, but time-consuming. A-posteriori Model Order Reduction methods can reduce computational time effectively. The choice of the reduced basis is crucial for accuracy. The SVD method is commonly used but time-consuming, while the MESS method provides an alternative. This paper compares these methods and other clustering approaches in a complex realistic problem. The quality of reduced bases and their impact on field distributions and global quantities are analyzed. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.