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Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a Nonlinear Poisson Structure. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. ESAIM: Mathematical Modelling and Numerical Analysis, 42(2):277–302, 2008. Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: Mathematical Modelling and Numerical Analysis, 47(3):859–873, 2013. Convergence Rates of the POD-Greedy Method. Reduced-basis Approximations and a Posteriori Error Estimation for Parabolic Partial Differential Equations. Theory and practice of finite elements, volume 159 of Applied Mathematical Sciences. Introduction to Symplectic and Hamiltonian Geometry. Preserving lagrangian structure in nonlinear model reduction with application to structural dynamics. Mathematical and Computational Applications, 24(2), 2019. Symplectic Model Order Reduction with Non- Orthonormal Bases. Structure-Preserving Model Order Reduction of Hamiltonian Systems for Linear Elasticity.
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Society for Industrial and Applied Mathematics, Philadelphia, PA, 2017. The results show that improvements of up to one order of magnitude in the relative reduction error are achievable with the new basis generation technique compared to the existing greedy approach from. In the numerical experiments, we compare the discussed methods for a linear elasticity problem. We prove that this algorithm computes a symplectic basis when symplectic techniques are used for compression. Inspired by POD-greedy, we use compression techniques in the greedy iterations to enrich the basis iteratively. We complement the procedure presented in with ideas of the POD-greedy, which results in a new greedy symplectic basis generation technique, the PSD-greedy. In our work, we discuss greedy algorithms for symplectic basis generation. It is based on a reduced-order basis that is symplectic, which requires symplectic basis generation techniques. For structure-preserving model order reduction (MOR) of Hamiltonian systems, symplectic MOR can be used. In numerical simulations of Hamiltonian systems, algorithms show improved accuracy when the symplectic structure is preserved. They are characterized by a phase-space, a symplectic form and a Hamiltonian function. When you have finished the entry, you can print the calendar you have made.Hamiltonian systems are central in the formulation of non-dissipative physical systems.