Symplectic Model-Reduction with a Weighted Inner (original) (raw)

In the recent years, considerable attention has been paid to preserving structures and 5 invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced 6 system. In the context of Hamiltonian systems, symplectic model reduction seeks to construct a 7 reduced system that preserves the symplectic symmetry of Hamiltonian systems. However, symplectic 8 methods are based on the standard Euclidean inner products and are not suitable for problems 9 equipped with a more general inner product. In this paper we generalize symplectic model reduction 10 to allow for the norms and inner products that are most appropriate to the problem while preserving 11 the symplectic symmetry of the Hamiltonian systems. To construct a reduced basis and accelerate 12 the evaluation of nonlinear terms, a greedy generation of a symplectic basis is proposed. Furthermore, 13 it is shown that the greedy approach yields a norm bounded reduced basis. The accuracy and the 14 stabi...