Article citations

    Veroy, K., Prud’homme, C. and Patera, A.T. (2003) Reduced-Basis Approximation of the Viscous Burgers Equation: Rigorous a Posteriori Error Bounds. Comptes Rendus de l’Académie des Sciences—Series I, 337, 619-624.

has been cited by the following article:

  • TITLE: A Real-Time Transient Analysis of a Functionally Graded Material Plate Using Reduced-Basis Methods
  • AUTHORS: Yonghui Huang, Yi Huang
  • KEYWORDS: Reduced-Basis Method, Transient Response, Functionally Graded Material, Hybrid Numerical Method, Real-Time
  • JOURNAL NAME: Advances in Linear Algebra & Matrix Theory DOI: 10.4236/alamt.2015.53010 Sep 08, 2015
  • ABSTRACT: Based on the hybrid numerical method (HNM) combining with a reduced-basis method (RBM), the real-time transient response of a functionally graded material (FGM) plates is obtained. The large eigenvalue problem in wavenumber domain has been solved through real-time off-line/on-line calculation. At off-line stage, a reduced-basis space is constructed in sample wavenumbers according to the solved eigenvalue problems. The matrices independent of parameters are projected onto the reduced-basis spaces. At on-line stage, the reduced eigenvalue problems of the arbitrary wavenumbers are built. Subsequently, the responses in wavenumber domain are obtained by the approximated eigen-pairs. Because of the application of RBM, the computational cost of transient displacement analysis of FGM plate is decreased significantly, while the accuracy of the solution and the physics of the structure are still retained. The efficiency and validity of the proposed method are demonstrated through a numerical example.