Reduced-order subscales for POD models

Reduced-Order Subscales for POD models

In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part which can be captured by the reduced-order model and the part which cannot, the subscales, for which a model is required. The proposed model for the subscales is defined as a linear function of the solution of the reduced-o...

Reduced order models based on local POD plus Galerkin projection

A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained vía POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estímate of the error of the Galerkin approximation. Several improvements are introduce...

Calibration of POD reduced-order models using Tikhonov regularization

AIAA 2001–0926 Investigation of Non-Linear Projection for POD Based Reduced Order Models for Aerodynamics

In this paper a method for inviscid airfoil analysis and design optimization using reduced order models has been reviewed, modifications to the methodology are proposed, and new results of flow computations and design optimization are presented. The goal of these reduced order models is to obtain solutions to the Euler equations with sufficient accuracy for design optimization, at a computation...

Efficient POD reduced-order modeling for parametrized nonlinear PDE systems

In this paper a model order reduction method for a nonlinear elliptic-parabolic system is developed. Systems of this type arise from mathematical models for lithium ion batteries. A non-intrusive reduced order approach based on proper orthogonal decomposition (POD) is presented. In addition to this the interpolation method introduced by Barrault et al. [3] is applied in order to achieve efficie...