Advances in Engineering Software
Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations
Journal of Computational Physics
Applied Numerical Mathematics
A method for aggregating state variables in large ecosystem models
Mathematics and Computers in Simulation
Using adaptive proper orthogonal decomposition to solve the reaction--diffusion equation
Applied Numerical Mathematics
Allocating power ground vias in 3D ICs for simultaneous power and thermal integrity
ACM Transactions on Design Automation of Electronic Systems (TODAES)
QLMOR: a new projection-based approach for nonlinear model order reduction
Proceedings of the 2009 International Conference on Computer-Aided Design
Atlas-based reduced models of blood flows for fast patient-specific simulations
STACOM'10/CESC'10 Proceedings of the First international conference on Statistical atlases and computational models of the heart, and international conference on Cardiac electrophysiological simulation challenge
Parameter identification in cardiac electrophysiology using proper orthogonal decomposition method
FIMH'11 Proceedings of the 6th international conference on Functional imaging and modeling of the heart
An Online Method for Interpolating Linear Parametric Reduced-Order Models
SIAM Journal on Scientific Computing
A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction
SIAM Journal on Numerical Analysis
Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
Journal of Computational and Applied Mathematics
Proper orthogonal decomposition for parameter estimation in oscillating biological networks
Journal of Computational and Applied Mathematics
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We investigate some basic properties of the proper orthogonal decomposition (POD) method as it is applied to data compression and model reduction of finite dimensional nonlinear systems. First we provide an analysis of the errors involved in solving a nonlinear ODE initial value problem using a POD reduced order model. Then we study the effects of small perturbations in the ensemble of data from which the POD reduced order model is constructed on the reduced order model. We explain why in some applications this sensitivity is a concern while in others it is not. We also provide an analysis of computational complexity of solving an ODE initial value problem and study the computational savings obtained by using a POD reduced order model. We provide several examples to illustrate our theoretical results.