Title A comparative study of several classical, discrete differential and isogeometric methods for solving Poisson’s equation on the disk /
Authors Nguyen, Thien ; Karčiauskas, Kęstutis ; Peters, Jörg
DOI 10.3390/axioms3020280
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Is Part of Axioms.. Basel : MDPI AG. 2014, Vol. 3, no. 2, p. 280-299.. ISSN 2075-1680
Keywords [eng] Poisson’s equation ; Digital geometry ; Isogeometric analysis ; Extraordinary points ; Singular parameterization ; G1 parameterization
Abstract [eng] This paper outlines and qualitatively compares the implementations of seven different methods for solving Poisson’s equation on the disk. The methods include two classical finite elements, a cotan formula-based discrete differential geometry approach and four isogeometric constructions. The comparison reveals numerical convergence rates and, particularly for isogeometric constructions based on Catmull–Clark elements, the need to carefully choose quadrature formulas. The seven methods include two that are new to isogeometric analysis. Both new methods yield O(h3) convergence in the L2 norm, also when points are included where n 6≠ 4 pieces meet. One construction is based on a polar, singular parameterization; the other is a G1 tensor-product construction.
Published Basel : MDPI AG
Type Journal article
Language English
Publication date 2014