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
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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.
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
- Gerard R. Richter, An inverse problem for the steady state diffusion equation, SIAM J. Appl. Math. 41 (1981), no. 2, 210–221. MR 628945, DOI https://doi.org/10.1137/0141016
- Kunio Tanabe, Projection method for solving a singular system of linear equations and its applications, Numer. Math. 17 (1971), 203–214. MR 293824, DOI https://doi.org/10.1007/BF01436376
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
- P. Dutt and S. Ta’asan, A spline-based parameter estimation technique for static models of elastic structures, Appl. Numer. Math. 5 (1989), no. 3, 161–175. MR 999238, DOI https://doi.org/10.1016/0168-9274%2889%2990032-9
- H. T. Banks and D. W. Iles, On compactness of admissible parameter sets: convergence and stability in inverse problems for distributed parameter systems, Control problems for systems described by partial differential equations and applications (Gainesville, Fla., 1986) Lect. Notes Control Inf. Sci., vol. 97, Springer, Berlin, 1987, pp. 130–142. MR 910511, DOI https://doi.org/10.1007/BFb0038747
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
G. R. Richter, An inverse problem for the steady state diffusion equation, SIAM J. Appl. Math. 41 (2), 1981
K. Tanabe, Projection methods for solving a singular system of linear equations and its applications, Numer. Math. 17, 203–214 (1971)
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
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)
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
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Article copyright:
© Copyright 1990
American Mathematical Society
