Naslov
Adaptive Multiresolution Method for Solving of PDEs

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

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

Izvornik
ICCES MM 2006 Program & Book of Abstracts / - Zagreb, 2006

Skup
ICCES Special Symposium on Meshless Methods

Mjesto i datum
Dubrovnik, Hrvatska, 14.06.2006. - 16.06.2006

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Fup basis functions; compact support; method of lines; collocation method; adaptive multiresolution approach; high gradients

Sažetak
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 efficiently to 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 the character of solution function and accuracy criteria. Numerical procedure is designed through a method of lines (MOL). The basic characteristic of the method is an adaptive multi-resolution approach in solving problems with different spatial and temporal scales and with desired level of accuracy using the entire family of Fup basis functions. Good performance of the proposed method is shown through the numerical examples by using few general advection dominated problems. The results demonstrate that the method is very convenient for solving engineering problems which require extensive computational resources, especially in describing sharp fronts or high gradients and changes of narrow transition zones in space and time.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Temeljne tehničke znanosti

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