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Space-time adaptive Fup multi-resolution approach for boundary-initial value problems


Gotovac, Hrvoje; Kozulić, Vedrana; Gotovac, Blaž
Space-time adaptive Fup multi-resolution approach for boundary-initial value problems // ICCES Special Symposium on Meshless & other novel computational methods
Suzhou, Kina, 2008. (pozvano predavanje, međunarodna recenzija, pp prezentacija, znanstveni)


Naslov
Space-time adaptive Fup multi-resolution approach for boundary-initial value problems

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

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Skup
ICCES Special Symposium on Meshless & other novel computational methods

Mjesto i datum
Suzhou, Kina, 13-17.10.2008.

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Boundary-initial value problems; collocation method; atomic basis functions; adaptive criterion

Sažetak
In this paper we show new space-time AFCM with resolved all space, but also time multiple scales. Essentially, AFCM solves PDE’ s and corresponding boundary conditions in the same way as FCT approximates a function by different resolution levels. All previous existing algorithms with wavelets and splines as well as recent form of the AFCM used localized basis functions only to obtain efficient adaptive strategy, but the PDE is solved by finite difference method on non-uniform adaptive grid (including all levels). In this paper, we present novel form of the AFCM with only Fup basis functions at each level using the collocation framework in space-time domain. 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