Nives Brajčić Kurbaša^*, Blaž Gotovac, Vedrana Kozulić

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 65-90, 2023, DOI:10.32604/cmes.2022.021940

Abstract The purpose of this paper is to present the class of atomic basis functions (ABFs) which are of exponential type and are denoted by . While ABFs of the algebraic type are already represented in the numerical modeling of various problems in mathematical physics and computational mechanics, ABFs of the exponential type have not yet been sufficiently researched. These functions, unlike the ABFs of the algebraic type , contain the tension parameter , which gives them additional approximation properties. Exponential monomials up to the th degree can be described exactly by the linear combination of the functions . The function… More >

Nives Brajčić Kurbaša¹, Blaž Gotovac¹, Vedrana Kozulić¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.6, pp. 493-530, 2016, DOI:10.3970/cmes.2016.111.493

Abstract This paper presents exponential Atomic Basis Functions (ABF), which are called Eup(x,ω). These functions are infinitely differentiable finite functions that unlike algebraic up(x) basis functions, have an unspecified parameter - frequency w. Numerical experiments show that this class of atomic functions has good approximation properties, especially in the case of large gradients (Gibbs phenomenon). In this work, for the first time, the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis. Application of… More >

V. Kozulić¹, H. Gotovac¹, B. Gotovac¹

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 51-70, 2007, DOI:10.3970/cmc.2007.006.051

Abstract In this paper, we present a multi-resolution adaptive algorithm for solving problems described by partial differential equations. The technique is based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions. As it is possible to calculate derivation values of Fup basis functions of high degree in a precise yet simple way, so it is possible to efficiently apply strong formulation procedures. The mesh free method developed in this work is named Adaptive Fup Collocation Method (AFCM). The distribution of collocation points within the observed area is changed adaptively, depending on… More >