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

5 Citations (Scopus)

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
Pages (from-to)139-154
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume325
DOIs
Publication statusPublished - 2017 Oct 1

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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