On the treatment of high-frequency issues in numerical simulation for dynamic systems by model order reduction via the proper orthogonal decomposition

R. Deokar, M. Shimada, C. Lin, K. K. Tamma

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

A new numerical strategy to remedy high-frequency issues caused by finite element discretization in structural dynamic problems has been proposed. A noteworthy characteristic of this advocated approach is that it is based upon the use of the proper orthogonal decomposition (POD) incorporated in conjunction with implicit or explicit numerically non-dissipative time integration schemes to substantially improve or eliminate undesirable effects due to high-frequency instabilities. Original systems with high-frequency issues are reduced via POD based on an adequate choice of a numerically dissipative scheme so that the resulting reduced systems contain no high-frequency participation. This approach confers the inherent advantages that numerically non-dissipative mechanical integrators, e.g., energy–momentum conserving or variational integrators, can be used to solve the reduced systems, fulfilling the requisite conservation laws in the projected basis and therefore provides a robust simulation. Linear and nonlinear numerical applications are shown to demonstrate the benefits and feasibility of this technique.

Original languageEnglish (US)
Pages (from-to)139-154
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume325
DOIs
StatePublished - Oct 1 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

Keywords

  • Computational dynamics
  • Proper orthogonal decomposition
  • Time integration

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