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

• 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
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-019-00915-w

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.