A Comparative Study of Several Classical, Discrete Differential and Isogeometric Methods for Solving Poisson’s Equation on the Disk

Axioms

Thien Nguyen²  Kȩstutis Karčiauskas¹ 

[1] Department of Mathematics, Vilnius University, LT-01513 Vilnius, Lithuania; E-Mail:;Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA; E-Mail:

关键词: Poisson’s equation;    digital geometry;    isogeometric analysis;    extraordinary points;    singular parameterization;    G¹ parameterization;   

DOI  :  10.3390/axioms3020280

来源: mdpi

【 摘 要 】

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 yieldtensor-product construction.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.