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 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.

Automated summary

This paper presents a suitable method for treating partial derivative equations, specifically the Laplace equation with Robin boundary conditions. The approach used is a nodal Hermite meshless collocation technique, incorporating radial basis functions to obtain shape functions and applying Hermite interpolation technique to impose boundary conditions directly, known as MRPHI. Trustworthy results were obtained through examples demonstrating the effectiveness of the method.