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## Solution Structure Method in Numerical Analysis of Engineering Problems

Kozulić, Vedrana
Solution Structure Method in Numerical Analysis of Engineering Problems // ACEX2015 ABSTRACT BOOK
Minhen, Njemačka, 2015. str. 71-71 (pozvano predavanje, međunarodna recenzija, sažetak, ostalo)

Naslov
Solution Structure Method in Numerical Analysis of Engineering Problems

Autori
Kozulić, Vedrana

Sažeci sa skupova, sažetak, ostalo

Izvornik
ACEX2015 ABSTRACT BOOK / - , 2015, 71-71

Skup
9th International Conference on Advanced Computational Engineering and Experimenting

Mjesto i datum
Minhen, Njemačka, 29.06.-02.07.2015

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Meshless method; solution structure; collocation; boundary conditions; atomic basis functions

Sažetak
Numerical methods are indispensable for the successful simulation of physical problems. Widely used mesh-based methods introduce a finite number of nodes to specify boundary conditions and perform numerical computations, and use spatial grids to approximate the geometric shape of a model. However, in modeling problems with complex geometry, difﬁculties often appear in creating good spatial grid that conforms to the shape of the model. To overcome this obstacle, a new class of numerical methods has been developed called meshfree or meshless methods. In this paper, we present a numerical method that combines solution structure method, atomic basis functions and a collocation technique. One of the major features of the proposed method is that it allows all prescribed boundary conditions to be satisﬁed exactly on all boundary points. Solution structure method is based on the theory of R-functions [1]. The basic idea of this procedure is to express the solution of a boundary value problem in the form of formulae called solution structures. Solution structure 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 informations about governing equation. In most practical situations, unknown differential component of the solution structure is represented by a linear combination of basis functions. Here, we propose to use atomic basis functions (ABFs) because of their good approximation properties. ABFs are infinitely-differentiable finite functions with compact support [2]. To determine the coefficients of linear combination in the solution structure, a collocation technique is used. The resulting meshfree method can be applied for solving boundary value problems in domains of arbitrarily complex geometry with complex boundary conditions. This paper summarizes the main principles of the method and presents numerical results for several simple test problems.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Temeljne tehničke znanosti