Model reduction for Smoluchowski equations with particle transfer

Timokhin, Ivan V.; Matveev, S. A.; Тыртышников, Е. Е.; Смирнов, А. П.

doi:10.1515/rnam-2021-0015

Cited by 3 publications

(1 citation statement)

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“…Firstly, the snapshot matrix becomes very large for problems with many time steps and parameter samples, leading to expensive singular-value decomposition (SVD). For this issue, methods such as the randomized SVD algorithm [31], fast adaptive cross-approximation [32], and local bases solutions method [33] have been used for large-scale problems. Beyond this, Wang et al [34] applied POD twice to reduce the cost of global spatial bases for unsteady flow problems in the parameter domain.…”

Section: Introductionmentioning

confidence: 99%

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

Li,

Pan,

Zhou

et al. 2023

Energies

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A new non-intrusive reduced-order modeling method based on space-time parameter decoupling for parametrized time-dependent problems is proposed. This method requires the preparation of a database comprising high-fidelity solutions. The spatial bases are extracted from the database through first-level proper orthogonal decomposition (POD). The algebraic relationship between the time trajectory/parameter positions and the projection coefficient is described by the linear superposition of the second-level POD bases (temporal bases) and the second-level projection coefficients (parameter-dependent coefficients). This decomposition strategy decouples the space-time parameter effects, providing a stable foundation for fast predictions of parametrized time-dependent problems. The mappings between the parameter locations and the parameter-dependent coefficients are approximated as Gaussian process regression (GPR) models. The accuracy and efficiency of the PPOD-ROM are demonstrated through two numerical examples: flows past a cylinder and turbine flows with a clocking effect.

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