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Numerical Solving of Boundary-Initial Value Problems using Space-Time Adaptive Fup Collocation Method


Gotovac, Hrvoje; Kozulić, Vedrana; Gotovac, Blaž
Numerical Solving of Boundary-Initial Value Problems using Space-Time Adaptive Fup Collocation Method // Proceedings of the 6th International Congress of Croatian Society of Mechanics / Smojver, Ivica ; Sorić, Jurica (ur.).
Zagreb: Hrvatsko društvo za mehaniku, 2009. str. 1-8 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)


Naslov
Numerical Solving of Boundary-Initial Value Problems using Space-Time Adaptive Fup Collocation Method

Autori
Gotovac, Hrvoje ; Kozulić, Vedrana ; Gotovac, Blaž

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of the 6th International Congress of Croatian Society of Mechanics / Smojver, Ivica ; Sorić, Jurica - Zagreb : Hrvatsko društvo za mehaniku, 2009, 1-8

ISBN
978-953-7539-10-8

Skup
6th International Congress of Croatian Society of Mechanics

Mjesto i datum
Dubrovnik, Hrvatska, 30.09.2009.-02.10.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Meshless method; boundary-initial value problem; collocation; atomic basis functions; adaptive procedure

Sažetak
This paper presents a new adaptive meshless method for solving boundary-initial value problems. Partial differential equations (PDE’s) are solved simultaneously in the space-time domain with resolved all space and time multiple scales. Numerical adaptive algorithm implements infinitely differentiable basis functions with compact support called Fup basis functions. Use of these functions enables an application of the procedure of a strong formulation. Here, the collocation technique is used. Each non-zero level solves only residual of the PDE from all previous levels and gives particular solution correction. Adaptive criterion adds new collocation points in the next level only in the space-time zones where solution correction is greater than the prescribed threshold. Numerical experiments with known analytic solutions show that solution correction on some level is greater than the difference between the analytic solution and overall solution up to that level. It means that an adaptive criterion directly estimates accuracy of the solution even if analytical solution is not a priori known. Moreover, this approach controls the global time integration error and enables a near optimal space-time adaptive grid which includes numerical efficiency and robustness.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Temeljne tehničke znanosti



POVEZANOST RADA


Projekt / tema
083-0831541-1534 - Adaptivno bezmrežno modeliranje u projektiranju građevinskih konstrukcija (Vedrana Kozulić, )

Ustanove
Fakultet građevinarstva, arhitekture i geodezije, Split