Certified Real-Time Solution of Parametrized Partial Differential Equations

  • Nguyen Ngoc Cuong
  • Karen Veroy
  • Anthony T. Patera


Engineering analysis requires the prediction of (say, a single) selected “output” se relevant to ultimate component and system performance:* typical outputs include energies and forces, critical stresses or strains, flowrates or pressure drops, and various local and global measures of concentration, temperature, and flux. These outputs are functions of system parameters, or “inputs”, μ, that serve to identify a particular realization or configuration of the component or system: these inputs typically reflect geometry, properties, and boundary conditions and loads; we shall assume that μ is a P-vector (or P-tuple) of parameters in a prescribed closed input domain D ⊂ ℝp. The input-output relationship se(μ): D → ℝ thus encapsulates the behavior relevant to the desired engineering context.


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Copyright information

© Springer 2005

Authors and Affiliations

  • Nguyen Ngoc Cuong
    • 1
  • Karen Veroy
    • 1
  • Anthony T. Patera
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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