Towards numerical solution of 3D problems by an efficient meshless method equipped with geometrical tools

In this paper, 3D problems are solved numerically by a meshless method using exponential bases functions. In the first place, starting from a uniform regular grid of points, with the availability of the information of Non-Uniform Rational B-Spline (NURBS) surfaces of a 3D geometry designed in the CAD programs, a fast point-in-membership test is conducted to identify the nodes located inside the domain. Thereafter, in the processing unit, the rational Exponential Basis Functions (EBFs) are used to approximate the unknown field in each local cloud. Finally, the system of equation is constructed by enforcing the pointwise compatibility and boundary conditions.

Keywords:

3D heat problem , grid generation , meshless.