Multilevel mesh free method for the torsion problem

Kozulić, Vedrana; Gotovac, B.; Colak, I.

doi:10.2507/daaam.scibook.2006.29

Cited by 2 publications

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“…Calculation of all required derivatives of function Fupn(x,y) can be written in an analogue form [16].…”

Section: Fig 4 Layout Of Fup4 Basis Functions In Relation To the Boundaries Of The One-dimensional Domainmentioning

confidence: 99%

“…Only points within the domain are collocation points; for points outside of the domain (black dots in Fig. 5b) recursive formulas are written according to (16) while the remaining points (white dots in Fig. 5b) are not included in the procedure.…”

Section: Example Of Homogeneous Dirichlet Problem: Torsion Problemmentioning

confidence: 99%

“…Practically good enough numerical solution is obtained on a grid that has a minimum number of collocation points within the domain that allows the implementation of the procedure of solution structure method with the selected basis functions. The minimum number of collocation points means that within a domain there is a core of 55 points which allows writing recursive equations (16). It defines uniform 1415 grid with 38 collocation points and a total of 176 equations.…”

Section: + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + mentioning

confidence: 99%

“…Rvachev and Rvachev [13], in their pioneering work, called these basis functions ˝atomic˝ because they span the vector spaces of all three fundamental functions in mathematics: algebraic, exponential and trigonometric polynomials. In numerical modelling, we applied Fup basis functions that belong to the atomic functions of algebraic type [16], [17], [18]. All derivatives of atomic Fup basis functions required by differential operators in the solution structure can be used directly in the numerical procedure.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Poisson’s Equation in an Arbitrary Domain by Using Meshless R-Function Method

Kozulić¹,

Gotovac²

2016

Proceedings of the 27th International DAAAM Symposium 2016

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This paper describes a numerical procedure that uses solution structure method, atomic basis functions and a collocation technique. Solution structure method is 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 basis functions. Here, we propose to use atomic basis functions because of their good approximation properties. To determine the coefficients of linear combination in the solution structure, a collocation technique is used. Combination of atomic basis functions and solution structure method gives the meshfree method that 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 proposed method and presents its application to solution of the torsion problem.

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“…Calculation of all required derivatives of function Fupn(x,y) can be written in an analogue form [16].…”

Section: Fig 4 Layout Of Fup4 Basis Functions In Relation To the Boundaries Of The One-dimensional Domainmentioning

confidence: 99%

Section: Example Of Homogeneous Dirichlet Problem: Torsion Problemmentioning

confidence: 99%

Section: + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Poisson’s Equation in an Arbitrary Domain by Using Meshless R-Function Method

Kozulić¹,

Gotovac²

2016

Proceedings of the 27th International DAAAM Symposium 2016

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“…Atomske bazne funkcije koriste se za rješavanje problema procesuiranja signala [33], [34], u analizi različitih problema strukturalne mehanike i matematičke fizike [1], [8], [9], [12], [13], [16], [26], [27], [28], [29], [30], [43], a zahvaljujući svojim svojstvima veoma uspješno se mogu primijeniti za rješavanje 1D i 2D problema [3], [10], [11], [24], [25]. Razvijena je i efikasna adaptivna Fup kolokacijska metoda koja je uspješno implementirana u problemima mehanike fluida i modeliranju rubno-početnih problema [14], [15], [17], [18], [19], [31], [32].…”

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Eksponencijalne atomske bazne funkcije : razvoj i primjena

Kurbaša¹

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In this work basic properties of algebraic Atomic Basis Functions (ABF) are systematized and, using analogous approach, ABF of exponential type, so far known only at the basic level, are developed. For the first time the properties of exponential ABFs are thoroughly investigated and expressions for calculating the values and all the necessary derivatives of the functions in an arbitrary points of the domain are developed as well as some special features required for their practical application in a form suitable for numerical analysis. A software module for calculating all necessary values of the exponential ABFs, including its own graphics support, is created within this work. Thus, the exponential ABF is prepared to use as users or compiler function. The presented 1D verification examples of the function approximation and the examples of solving differential equations illustrate and confirm the practical advantage of the ABFs of the exponential type in relation to the, so far mostly used, algebraic functions, especially for describing expressed fronts and/or waves contained in the numerical solutions of various technical tasks.

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Multilevel mesh free method for the torsion problem

Cited by 2 publications

References 0 publications

Numerical Solution of Poisson’s Equation in an Arbitrary Domain by Using Meshless R-Function Method

Numerical Solution of Poisson’s Equation in an Arbitrary Domain by Using Meshless R-Function Method

Eksponencijalne atomske bazne funkcije : razvoj i primjena

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