Data discovering of inverse Robin boundary conditions problem in arbitrary connected domain through meshless radial point Hermite interpolation

In this paper, a suitable method is presented to treat the partial derivative equations, especially the Laplace equation having the Robin boundary conditions. These equations come from classical physics, especially the branch of thermodynamics, and have an efficient role in the field of heat and tem...

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Bibliographic Details
Published in:Engineering with computers 2021-07, Vol.37 (3), p.1821-1833
Main Authors: Seblani, Youssef El, Shivanian, Elyas
Format: Article
Language:English
Subjects:
Boundary conditions
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Domains
Interpolation
Laplace equation
Math. Applications in Chemistry
Mathematical analysis
Mathematical and Computational Engineering
Meshless methods
Original Article
Radial basis function
Shape functions
Systems Theory
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Summary:In this paper, a suitable method is presented to treat the partial derivative equations, especially the Laplace equation having the Robin boundary conditions. These equations come from classical physics, especially the branch of thermodynamics, and have an efficient role in the field of heat and temperature. Our motivation is to reset a harmonic data obtained from Robin’s conditions in the arbitrary plane domain particularly on its boundaries. The applied method is a nodal Hermite meshless collocation technique at which it is formed of radial basis functions to get out the shape functions which is the key to construct the local bases in the neighborhoods of the nodal points. Moreover, by taking into consideration the Hermite interpolation technique, we can impose the boundary conditions directly, the named technique is called “MRPHI,” meshless radial point Hermite interpolation, and it is done on some examples so that trustworthy results are obtained.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-019-00915-w