Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Computers & Mathematics with Applications
Nonlinear Model Reduction via Discrete Empirical Interpolation
SIAM Journal on Scientific Computing
Asymptotic error expansions for hypersingular integrals
Advances in Computational Mathematics
Non-linear model reduction for the Navier-Stokes equations using residual DEIM method
Journal of Computational Physics
| Hi-index | 0.09 |
A new scheme for implementing a reduced order model for complex mesh-based numerical models (e.g. finite element unstructured mesh models), is presented. The matrix and source term vector of the full model are projected onto the reduced bases. The proper orthogonal decomposition (POD) is used to form the reduced bases. The reduced order modeling code is simple to implement even with complex governing equations, discretization methods and nonlinear parameterizations. Importantly, the model order reduction code is independent of the implementation details of the full model code. For nonlinear problems, a perturbation approach is used to help accelerate the matrix equation assembly process based on the assumption that the discretized system of equations has a polynomial representation and can thus be created by a summation of pre-formed matrices. In this paper, by applying the new approach, the POD reduced order model is implemented on an unstructured mesh finite element fluid flow model, and is applied to 3D flows. The error between the full order finite element solution and the reduced order model POD solution is estimated. The feasibility and accuracy of the reduced order model applied to 3D fluid flows are demonstrated.