Numerical Algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow

We consider three integral observations inverse problems (IP1, IP2, IP3) for reconstruction of a time-dependent convection coefficient and a source in magnetohydrodynamics (MHD) model. On the first stage, using the integral observations, we reduce the inverse problems to nonclassical direct (forward...

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Bibliographic Details
Published in:Algorithms 2024-09, Vol.17 (9), p.387
Main Authors: Kandilarov, Juri D., Vulkov, Lubin G.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Boundary conditions
Convection
Flow velocity
Heat
inverse problem
Inverse problems
Linear systems
Magnetic fields
Magnetohydrodynamics
Mathematical models
Methods
numerical algorithms
Numerical analysis
Parameter estimation
Partial differential equations
Reynolds number
Time dependence
Viscosity
Well posed problems
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Summary:We consider three integral observations inverse problems (IP1, IP2, IP3) for reconstruction of a time-dependent convection coefficient and a source in magnetohydrodynamics (MHD) model. On the first stage, using the integral observations, we reduce the inverse problems to nonclassical direct (forward) ones. The equivalence between the inverse and direct problems is established. Then, the well-posedness of nonclassical problems is proved. Further, to overcome the difficulties arising from the nonlinear nonlocal parabolic operators, we construct a linarization algorithm in time after their difference space discretizatons. Next, on each iteration, to solve the corresponding linear systems of algebraic equations, we propose adequate fast elimination algorithms. Computational results of test examples data are discussed.
ISSN:1999-4893
1999-4893
DOI:10.3390/a17090387