Selective proper orthogonal decomposition model reduction for forming simulations

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...

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 ...

Reduction of Model Order Based on Proper Orthogonal Decomposition for Lithium-Ion Battery Simulations

A reduced-order model ROM is developed using proper orthogonal decomposition POD for a physics-based lithium-ion battery model. The methodology to obtain the proper orthogonal modes and to analyze their optimality is included. The POD-based ROM for a lithium-ion battery is used to simulate a charge/discharge process and the behavior of a battery pack. Compared to the physics-based model, the co...

Balanced Model Reduction via the Proper Orthogonal Decomposition

A new method for performing a balanced reduction of a high-order linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshots is used to obtain low-rank, reduced-rangeapproximationsto the system controllabilityand observability grammiansin either the timeor frequency domain.The approximationsare the...