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Symplectic Model Order Reduction with Non-Orthonormal Bases
Parametric high-fidelity simulations are of interest for a wide range of applications. However, the restriction of computational resources renders such models to be inapplicable in a real-time
Second Order Conformal Symplectic Schemes for Damped Hamiltonian Systems
TLDR
Numerical methods for solving linearly damped Hamiltonian systems are constructed using the popular Störmer–Verlet and implicit midpoint methods, and additional structure preservation is discovered for the discretized PDEs.
Structure-preserving Exponential Runge-Kutta Methods
TLDR
Numerical experiments illustrate the higher-order accuracy and structure-preserving properties of various ERK methods, demonstrating clear advantages over classical conservative Runge--Kutta methods.
MULTIPLE SCALES AND ENERGY ANALYSIS OF COUPLED RAYLEIGH-VAN DER POL OSCILLATORS WITH TIME-DELAYED DISPLACEMENT AND VELOCITY FEEDBACK: HOPF BIFURCATIONS AND AMPLITUDE DEATH
In this paper, two classes of techniques, based on multiple scales perturbation analysis and the averaged energy (or Lyapunov function) method, are employed to investigate interesting nonlinear
Symplectic Model-Reduction with a Weighted Inner Product
In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In
Error Estimation for the Simulation of Elastic Multibody Systems
TLDR
The error bounds used in elastic multibody system (EMBS) described in the floating frame of reference formulation are reviewed, with a view to evaluating substructures / surrogate models for system level simulations.
Model Order Reduction of an Elastic Body Under Large Rigid Motion
A parametrized equation of motion in the absolute coordinate formulation is derived for an elastic body with large rigid motion using continuum mechanics. The resulting PDE is then discretized using
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