Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Parameter estimation problems for distributed systems using a multigrid method

Authors: Shlomo Ta'asan and Pravir Dutt
Journal: Quart. Appl. Math. 48 (1990), 387-396
MSC: Primary 65K99; Secondary 65P05
DOI: https://doi.org/10.1090/qam/1052143
MathSciNet review: MR1052143
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of estimating spatially varying coefficients of partial differential equations from observation of the solution and of the right-hand side of the equation. We assume that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

References [Enhancements On Off] (What's this?)

  • [1] H. T. Banks, A survey of some problems and recent results for parameter estimation and optimal control in delay and distributed parameter systems, ICASE Report No. 81-26
  • [2] G. R. Richter, An inverse problem for the steady state diffusion equation, SIAM J. Appl. Math. 41 (2), 1981 MR 628945
  • [3] K. Tanabe, Projection methods for solving a singular system of linear equations and its applications, Numer. Math. 17, 203-214 (1971) MR 0293824
  • [4] A. Brandt, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Monograph available as GMD-Study, no. 85, from GMD-F1T, Postfach 1240, D-5205, St. Augustin 1, W. Germany
  • [5] P. Dutt and S. Ta'asan, A spline-based parameter estimation technique for static models of elastic structures, Appl. Numer. Math. 5, 161-175 (1989) MR 999238
  • [6] H. T. Banks and D. W. Iles, On compactness of admissible parameter sets: Convergence and stability in inverse problems for distributed systems, ICASE Report No. 86-38, NASA CR-178128, 1986 MR 910511

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 65K99, 65P05

Retrieve articles in all journals with MSC: 65K99, 65P05

Additional Information

DOI: https://doi.org/10.1090/qam/1052143
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society