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arXiv · 2308.02625

Linearly Implicit Global Energy Preserving Reduced-order Models for Cubic Hamiltonian Systems

Süleyman Yildiz·Pawan Goyal·Peter Benner
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Abstract

This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to construct reduced-order models in the form of Hamiltonian systems suitable for long-time integration. Furthermore, We prove that the constructed reduced-order models preserve global energy, and the spatially discrete equations also preserve the spatially-discrete local energy conversation law. We illustrate the efficiency of the proposed method using three numerical examples, namely a linear wave equation, the Korteweg-de Vries equation, and the Camassa-Holm equation, and present a comparison with the classical POD-Galerkin method.

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Süleyman Yildiz, Pawan Goyal, Peter Benner. 2023-08-04. Linearly Implicit Global Energy Preserving Reduced-order Models for Cubic Hamiltonian Systems. https://arxiv.org/abs/2308.02625

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