Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
A reduced-order method for simulation and control of fluid flows
Journal of Computational Physics
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
SIAM Journal on Numerical Analysis
A New Look at Proper Orthogonal Decomposition
SIAM Journal on Numerical Analysis
Nonlinear Model Reduction via Discrete Empirical Interpolation
SIAM Journal on Scientific Computing
Modeling and control of physical processes using proper orthogonal decomposition
Mathematical and Computer Modelling: An International Journal
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A new method for enhanced surrogate modeling of complex systems by exploiting gradient information is presented. The technique combines the proper orthogonal decomposition (POD) and interpolation methods capable of fitting both sampled input values and sampled derivative information like Kriging (aka spatial Gaussian processes). In contrast to existing POD-based interpolation approaches, the gradient-enhanced method takes both snapshots and partial derivatives of snapshots of the associated full-order model (FOM) as an input. It is proved that the resulting predictor reproduces these inputs exactly up to the standard POD truncation error. Hence, the enhanced predictor can be considered as (approximately) first-order accurate at the snapshot locations. The technique applies to all fields of application, where derivative information can be obtained efficiently, for example via solving associated primal or adjoint equations. This includes, but is not limited to Computational Fluid Dynamics (CFD). The method is demonstrated for an academic test case exhibiting the main features of reduced-order modeling of partial differential equations.