Matrix computations (3rd ed.)
A reduced-order method for simulation and control of fluid flows
Journal of Computational Physics
A New Look at Proper Orthogonal Decomposition
SIAM Journal on Numerical Analysis
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Error Estimation for Reduced-Order Models of Dynamical Systems
SIAM Journal on Numerical Analysis
The Effect of Problem Perturbations on Nonlinear Dynamical Systems and their Reduced-Order Models
SIAM Journal on Scientific Computing
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Reduced-order models for parameter dependent geometries based on shape sensitivity analysis
Journal of Computational Physics
Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
SIAM Journal on Scientific Computing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon.