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

Tags

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design

Technology Areas

  • Space