engleski

Numerical modeling of the boundary value problems using the R-function method and Atomic basis functions

In this paper the meshless numerical model for solving boundary value problems using the R-function method is developed. R-function method is based on the idea of the reverse procedure for determining analytic and approximate solutions of mathematical physics problems. Rvachev developed so called “semi-algebra” [10] which allows accurate description of the geometry of the domain, accurate description of all boundary conditions and zones with different properties of material. To describe the problem mathematically, the so called “solution structure” [11] is constructed. Solution structure depends on three components: the first component describes the geometry of the domain, the second component describes all boundary conditions exactly, while the third component is the only unknown component and is called the differential component, because the operator from the differential equation acts on it. To determine the differential component in the solution structure algebraic polynomials and atomic basis functions Fupn(x), [2], [4], are used. Functions Fupn(x) are infinitely derivable finite basis functions which are elements of the universal space UPn. R-function method, in which for the first time the atomic basis functions are implemented using a strong formulation, is illustrated on the torsion problem of circular prismatic bar.

Boundary value problem; R-function method; Solution structure; Atomic basis functions; Torsion of prismatic bars

nije evidentirano