Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems

• Published in: Advances in computational mathematics Vol. 50; no. 1
• Main Authors: Herkert, Robin, Buchfink, Patrick, Haasdonk, Bernard
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2024; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Dictionaries; Dynamical systems; Hamiltonian functions; Interpolation; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Model reduction; MORe 2022; Smart structures; Visualization; Wave equations; 93A15; Hamiltonian systems; 65P10; Symplectic model reduction; 37M15; 34C20; Dictionary-based approximation; Energy preservation; 78M34
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-023-10102-7

Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n -widths. Additionally, Hamiltonian structure of dynamical systems may be available and should be preserved during the reduction. In the current presentation, we address these two aspects by proposing a corresponding dictionary-based, online-adaptive MOR approach. The method requires dictionaries for the state-variable, non-linearities, and discrete empirical interpolation (DEIM) points. During the online simulation, local basis extensions/simplifications are performed in an online-efficient way, i.e., the runtime complexity of basis modifications and online simulation of the reduced models do not depend on the full state dimension. Experiments on a linear wave equation and a non-linear Sine-Gordon example demonstrate the efficiency of the approach.