Chaotic dynamics of coherent structures
Proceedings of the eighth annual international conference of the Center for Nonlinear Studies on Advances in fluid turbulence
SIAM Journal on Scientific Computing
Circumventing Storage Limitations in Variational Data Assimilation Studies
SIAM Journal on Scientific Computing
Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
Journal of Optimization Theory and Applications
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Adaptive Reduced-Order Controllers for a Thermal Flow System Using Proper Orthogonal Decomposition
SIAM Journal on Scientific Computing
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
Comparative Study with Data Assimilation Experiments Using Proper Orthogonal Decomposition Method
Large-Scale Scientific Computing
Journal of Computational and Applied Mathematics
A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation
Applied Numerical Mathematics
Applied Numerical Mathematics
Linearized reduced-order models for subsurface flow simulation
Journal of Computational Physics
Numerical simulations with data assimilation using an adaptive POD procedure
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Finite Elements in Analysis and Design
POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow
Computers & Mathematics with Applications
Computers & Mathematics with Applications
POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model
Journal of Computational Physics
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The proper orthogonal decomposition (POD) is shown to be an efficient model reduction technique for simulating physical processes governed by partial differential equations. In this paper, we make an initial effort to investigate problems related to POD reduced modeling of a large- scale upper ocean circulation in the tropic Pacific domain. We construct different POD models with different choices of snapshots and different number of POD basis functions. The results from these different POD models are compared with that of the original model. The main findings are: (1) the large-scale seasonal variability of the tropic Pacific obtained by the original model is well captured by a low dimensional system of order 22, which is constructed using 20 snapshots and 7 leading POD basis functions. (2) the RMS errors for the upper ocean layer thickness of the POD model of order 22 are less than 1m that is less than 1% of the average thickness and the correlation between the upper ocean layer thickness with that from the POD model is around 0.99. (3) Retaining modes that capture 99% energy is necessary in order to construct POD models yielding a high accuracy.