Structure-Preserving Model-reduction
Abstract
The formulation of accurate and stable reduced order models (ROM) for time-dependent problems continues to pose substantial challenges, in particular for problems with limited inherent dissipation. Indeed, it is well known that following a standard approach, based on a proper orthogonal decomposition or a greedy approach, leads to unstable models, even when applied to linear problems such as the wave equation. In this effort, we shall address this generic problem by developing techniques to formulate stable reduced order models for time-dependent problems by carefully constructing the reduced model such that it inherits certain inherent properties of the dynamical problems, e.g., energy, conservation etc. This is fundamentally different from existing methods in which the linear space, used to represent the solution, is developed without knowledge of the underlying problem. Initial examples and analysisconfirm that this approach ensures stability and also yields models of overall higher accuracy.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 11, 2017
- Source ID
- FA95501710241
Entities
People
- Jan S. Hesthaven
Organizations
- Air Force Office of Scientific Research
- Swiss Federal Institute of Technology in Lausanne
- United States Air Force