A Laplace Transform Certified Reduced Basis Method; Application to the Heat Equation and Wave Equation

Abstract

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary "modal" truncation; RB eigenfunction decomposition and contour integration for Offline-Online decomposition. We present numerical results to demonstrate the accuracy and efficiency of the approach.

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Document Details

Document Type
Technical Report
Publication Date
Feb 21, 2011
Accession Number
ADA557532

Entities

People

  • A. T. Patera
  • D. B. Huynh
  • D. J. Knezevic

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Coefficients
  • Decomposition
  • Eigenvalues
  • Eigenvectors
  • Engineering
  • Equations
  • Frequency
  • Hilbert Space
  • Information Operations
  • Modal Analysis
  • Standards
  • Time Domain
  • Wave Equations

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Positioning, Navigation, and Timing (PNT) Technology.