Adaptive Multiresolution Method for Solving of PDEs (CROSBI ID 527004)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Kozulić, Vedrana ; Gotovac, Hrvoje ; Gotovac, Blaž
engleski
Adaptive Multiresolution Method for Solving of PDEs
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.
Fup basis functions; compact support; method of lines; collocation method; adaptive multiresolution approach; high gradients
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Podaci o prilogu
33-x.
2006.
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objavljeno
Podaci o matičnoj publikaciji
ICCES MM 2006 Program & Book of Abstracts
Zagreb:
Podaci o skupu
ICCES Special Symposium on Meshless Methods
predavanje
14.06.2006-16.06.2006
Dubrovnik, Hrvatska