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Model reduction in Smoluchowski-type equations

  • Ivan V. Timokhin EMAIL logo , Sergey A. Matveev , Eugene E. Tyrtyshnikov und Alexander P. Smirnov
Veröffentlicht/Copyright: 17. Februar 2022

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.

MSC 2010: 65L05

Acknowledgment

The authors are grateful to Nikolai Zamarashkin for comprehensive discussions during preparation of this work.

  1. Funding: Ivan Timokhin was supported by Moscow Center of Fundamental and Applied Mathematics (agreement with the Ministry of Education and Science of the Russian Federation No. 075–15–2019–1624). Eugene Tyrtyshnikov and Sergey Matveev were supported by the Russian Science Foundation, grant No. 19–11–00338.

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Received: 2021-09-02
Accepted: 2021-11-22
Published Online: 2022-02-17
Published in Print: 2022-02-23

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