IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

POD Reduced-Order Model for Time-Fractional Partial Differential Equations and its Applications in Parameter Identification

  • Aug. 22, 2016
  • 1:15 p.m.
  • LeConte 312

Abstract

In this talk, a reduced-order model (ROM) based on the proper orthogonal decomposition (POD) method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). We demonstrate the effectiveness of the POD-ROM by several numerical examples, in which the ROM achieves the same accuracy of the full-order model (FOM) over a long-term simulation while greatly reducing the computational cost. The proposed ROM is then regarded as a surrogate of FOM and is applied to an inverse problem for identifying the order of the time-fractional derivative of the TFPDE model. Based on the Levenberg--Marquardt regularization iterative method with the Armijo rule, we develop a ROM-based algorithm for solving the inverse problem. For cases in which the observation data is either uncontaminated or contaminated by random noise, the proposed approach is able to achieve accurate parameter estimation efficiently.

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