Sinc-Galerkin Estimation of Diffusivity in Parabolic Problems

Abstract

A fully Sinc Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an appropriate value of the regularization parameter is briefly discussed, and numerical examples are given which demonstrate the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1991
Accession Number
ADA237202

Entities

People

  • Kenneth L. Bowers
  • Ralph C. Smith

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Coefficients
  • Convergence
  • Data Sets
  • Differential Equations
  • Diffusion
  • Diffusion Coefficient
  • Engineering
  • Equations
  • Errors
  • Galerkin Method
  • Guarantees
  • Measurement
  • Noise
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)