Model Variational Inverse Problems Governed by Partial Differential Equations

Abstract

We discuss solution methods for inverse problems, in which the unknown parameters are connected to the measurements through a partial differential equation (PDE). Various features that commonly arise in these problems, such as inversions for a coefficient field, for the initial condition in a time-dependent problem, and for source terms are being studied in the context of three model problems. These problems cover distributed, boundary, as well as point measurements, different types of regularizations, linear and nonlinear PDEs, and bound constraints on the parameter field. The derivations of the optimality conditions are shown and efficient solution algorithms are presented. Short implementations of these algorithms in a generic finite element toolkit demonstrate practical strategies for solving inverse problems with PDEs. The complete implementations are made available to allow the reader to experiment with the model problems and to extend them as needed.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2011
Accession Number
ADA555315

Entities

People

  • Georg Stadler
  • Noei Petra

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Equations Of State
  • Inverse Problems
  • Inversion
  • Lagrangian Functions
  • Linear Systems
  • Measurement
  • Navier Stokes Equations
  • Notation
  • Partial Differential Equations
  • Steepest Descent Method

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.