Abstract
The method of Proper Orthogonal Decompositions (POD) is a data-based method that is suitable for the reduction of large-scale distributed systems. In this paper we propose a generalization of the POD method so as to take the ND nature of a distributed model into account. This results in a novel procedure for model reduction of systems with multiple independent variables. Data in multiple independent variables is associated with the mathematical structure of a tensor. We show how orthonormal decompositions of this tensor can be used to derive suitable projection spaces. These projection spaces prove useful for determining reduced order models by performing Galerkin projections on equation residuals. We demonstrate how prior knowledge about the structure of the model reduction problem can be used to improve the quality of approximations. The tensor decomposition techniques are demonstrated on an application in data compression. The proposed model reduction procedure is illustrated on a heat diffusion problem.
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This work is supported by the Dutch Technologiestichting STW under project number EMR.7851.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van Belzen, F., Weiland, S. A tensor decomposition approach to data compression and approximation of ND systems. Multidim Syst Sign Process 23, 209–236 (2012). https://doi.org/10.1007/s11045-010-0144-x
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DOI: https://doi.org/10.1007/s11045-010-0144-x