Naslov
A new approach to solving boundary value problems in arbitrarily bounded domains

Autori
Kozulić, Vedrana ; Gotovac, Blaž ; Brajčić Kurbaša, Nives

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, prošireni sažetak, znanstveni

Izvornik
Book of Abstracts of the 10th ICCSM International Congress of Croatian Society of Mechanics / Skozrit, Ivica ; Sorić, Jurica ; Tonković, Zdenko - Zagreb : Hrvatsko društvo za mehaniku (HDM), 2022, 169-170

Skup
10th International Congress of Croatian Society of Mechanic (ICCSM 2022)

Mjesto i datum
Pula, Hrvatska, 28.09.2022. - 30.09.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
collocation method, atomic basis functions, Dirichlet boundary condition, Neumann boundary condition

Sažetak
In this paper, a new algorithm is presented to solve the boundary value problems on general domains. The approach combines the collocation method and atomic basis functions of algebraic type called Fup functions. This choice of basis functions provides smooth approximation on regular grids. All conditional equations related to the boundary of the domain are written at the collocation points on a stepped polygon inscribed in the given domain. The known value of the boundary condition at a point on the boundary of the domain is satisfied from the collocation point inside the domain in such a way that the Dirichlet or Neumann boundary condition develops into the Taylor series. The method is particularly successful in combination with Rvachev's theory of R-functions that provide a powerful tool for accurate geometry description. Numerical examples are given to demonstrate the efficiency and feasibility of the proposed method. The expected rates of convergence of the numerical solution as well as its derivatives are confirmed.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Temeljne tehničke znanosti

POVEZANOST RADA