A constrained proper orthogonal decomposition model for upscaling permeability

Model Reduction via Proper Orthogonal Decomposition

Model Reduction by Proper Orthogonal Decomposition (POD)

Mathematical models for human tissue and blood flow both represent time dependent nonlinear partial differential equations in three space dimensions. Their numerical solution based on appropriate space/time discretizations requires computational times that even when using state-of-the-art algorithmic solvers are far from being acceptable for real time OR scenarios. A way to overcome this diffic...

Proper Orthogonal Decomposition for Model Updating of Nonlinear Mechanical Systems

Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve decomposition, is emerging as a useful experimental tool in dynamics and vibrations. The POD is a means of extracting spatial information from a set of time series data available on a domain. The use of Karhunen-Loeve (K-L) transform is of great help in nonlinear settings where traditional linear techniques such as modal testin...

Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition

Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition ...

Artificial viscosity proper orthogonal decomposition

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standardmodels created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a s...