Preprint Article Version 1 This version is not peer-reviewed

Toward Optimality of Proper Generalised Decomposition Bases

Version 1 : Received: 31 January 2019 / Approved: 1 February 2019 / Online: 1 February 2019 (10:41:27 CET)

A peer-reviewed article of this Preprint also exists.

Alameddin, S.; Fau, A.; Néron, D.; Ladevèze, P.; Nackenhorst, U. Toward Optimality of Proper Generalised Decomposition Bases. Math. Comput. Appl. 2019, 24, 30. Alameddin, S.; Fau, A.; Néron, D.; Ladevèze, P.; Nackenhorst, U. Toward Optimality of Proper Generalised Decomposition Bases. Math. Comput. Appl. 2019, 24, 30.

Journal reference: Math. Comput. Appl. 2019, 24, 30
DOI: 10.3390/mca24010030

Abstract

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

Subject Areas

model order reduction (MOR); low-rank approximation; proper generalised decomposition (PGD); PGD compression; randomised SVD; nonlinear material behaviour.

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