Model reduction in Smoluchowski-type equations

Abstract

In the present paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a low-dimensional space allowing to approximate the solutions of aggregation equations. We also demonstrate that it is possible to model the aggregation process with the complexity depending only on dimension of such a space but not on the original problem size. In addition, we propose a method for reconstruction of the necessary space without solving of the full evolutionary problem, which can lead to significant acceleration of computations, examples of which are also presented.

Non-Intrusive Reduced-Order Modeling Based on Parametrized Proper Orthogonal Decomposition

“…Then, these RBs span a reduced subspace with a significantly smaller rank compared to high-fidelity dynamical systems. The greedy algorithm [8][9][10] and some modal decompositions, such as dynamic mode decomposition (DMD) [11][12][13] and proper orthogonal decomposition (POD) [14][15][16][17][18][19][20], are popular approaches for extracting the RBs. In the greedy algorithm, a set of snapshots is selected as the bases by utilizing an error estimator and an optimal criterion [21][22][23].…”