Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition

Proper Orthogonal Decomposition Model Order Reduction of nonlinear IC models

Future simulation for nanoelectronics requires that circuit equations can be coupled to electromagnetics, to semiconductor equations, and to heat transfer. The consequence is that one has to deal with large systems. Model Order Reduction (MOR) is a means to speed up simulation of large systems. Existing MOR techniques mostly apply to linear problems and even then they have to be generalized to ...

Model Reduction via Proper Orthogonal Decomposition

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...

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...

Nonlinear Robust and Optimal Control Via Proper Orthogonal Decomposition

In this paper, a methodology based on proper orthogonal decomposition (POD) for computing approximate closed-loop optimal or robust control laws for finite-dimensional nonlinear systems is proposed. The solution can be obtained on any arbitrary domain of the state space represented by a multidimensional grid. The method only requires the computation of a limited number of well-conditioned two-p...