The applicability of model order reduction based on proper orthogonal decomposition to problems in dynamic thermoelasticity with multiple subdomains

D. Maxam, R. Deokar, Kumar K Tamma

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A robust proper orthogonal decomposition technique is applied to develop reduced-order models (ROMs) for time-dependent thermal stress problems that are arbitrarily discretized with multiple sub-domains to provide flexibility and generality in the sense that different spatial methods and different time integration algorithms can be employed in a single analysis. This approach enables large computational savings for model problems with either/both transient thermal and dynamic structural effects by reducing the degrees of freedom with minimal losses to accuracy. The method of snapshots is used to construct a reduced-order basis from a short training simulation of the full-order model (FOM) which selectively preserves only the relevant physical characteristics of the solution. The approach is described in detail for both first- and second-order ordinary differential equations and differential algebraic equations, such as arising from problems with multiple sub-domains, and the solution of the FOM and ROM by the state-of-the-art GSSSS framework of algorithms is described. Numerical examples in thermal transport, quasi-static thermal stresses, and thermally-induced vibrations for single domains and multiple domains via the finite element method (other methods within each sub-domain can also be integrated with FEM but are not discussed here) illustrate the robustness and utility of the proposed methodology.

Original languageEnglish (US)
Pages (from-to)744-768
Number of pages25
JournalJournal of Thermal Stresses
Volume42
Issue number6
DOIs
StatePublished - Jun 3 2019

Keywords

  • Differential algebraic equation
  • dynamics
  • subdomain
  • thermally-induced vibrations
  • thermoelasticity
  • time integration; reduced-order modeling

Fingerprint Dive into the research topics of 'The applicability of model order reduction based on proper orthogonal decomposition to problems in dynamic thermoelasticity with multiple subdomains'. Together they form a unique fingerprint.

Cite this