Numerical study of the coefficient identification algorithm based on ensembles of adjoint problem solutions for a production-destruction model
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Alexey V. Penenko
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Zhadyra S. Mukatova
Abstract
A numerical algorithm for the solution of an inverse coefficient problem for nonstationary, nonlinear production-destruction type model is proposed and tested on an example of the Lorenz’63 system. With an ensemble of adjoint problem solutions, the inverse problem is transformed into a quasi-linear matrix problem and solved with Newton-type algorithm. Two different ways of the adjoint ensemble construction are compared. In the first one, a trigonometric basis is used. In the second one in situ measurements are taken into account. Local convergence properties of the algorithm are studied numerically to find out when the use of more data can lead to the degradation of the reconstruction results.
Funding source: Russian Science Foundation
Funding source: Russian Foundation for Basic Research
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The work was supported by RSF project 17-71-10184 in the part of the algorithms development with Fourier-type data reduction and by RFBR project 19-07-01135 in the part of the algorithms development and numerical analysis for inverse coefficient problems with point-wise data reduction.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- A reliable numerical approach for nonlinear fractional optimal control problems
- Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions
- Ground state solutions for nonlinear fractional Kirchhoff–Schrödinger–Poisson systems
- Existence and uniqueness of solutions for coupled systems of Liouville-Caputo type fractional integrodifferential equations with Erdélyi-Kober integral conditions
- Optimization of exact controllability for fractional impulsive partial stochastic differential systems via analytic sectorial operators
- Numerical study of the coefficient identification algorithm based on ensembles of adjoint problem solutions for a production-destruction model
- Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)
Articles in the same Issue
- Frontmatter
- Original Research Articles
- A reliable numerical approach for nonlinear fractional optimal control problems
- Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions
- Ground state solutions for nonlinear fractional Kirchhoff–Schrödinger–Poisson systems
- Existence and uniqueness of solutions for coupled systems of Liouville-Caputo type fractional integrodifferential equations with Erdélyi-Kober integral conditions
- Optimization of exact controllability for fractional impulsive partial stochastic differential systems via analytic sectorial operators
- Numerical study of the coefficient identification algorithm based on ensembles of adjoint problem solutions for a production-destruction model
- Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)
