engleski

MESHLESS METHOD BASED ON THE R-FUNCTIONS AND ATOMIC BASIS FUNCTIONS FOR THE SOLUTION OF TWO-DIMENSIONAL BOUNDARY VALUE PROBLEMS

This paper presents a meshless method based on the theory of R-functions. The solution of a boundary value problem is expressed in the form of formulae called solution structure which depends on three components: the first component describes the geometry of the domain exactly in analytical form, the second describes all boundary conditions exactly, while the third component is called differential component because it contains information about governing equation. Unknown differential component of the solution structure is represented by a linear combination of atomic basis functions which are infinitely differentiable functions with compact support. To determine the coefficients of linear combination in the solution structure, a collocation technique is used. The proposed method is applied to solve the torsion problem of a prismatic bar.

meshless method ; solution structure ; collocation ; boundary conditions ; atomic functions

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