A Comparative Study of Several Classical, Discrete Differential and Isogeometric Methods for Solving Poisson’s Equation on the Disk
| Autor: | Jörg Peters, Thien Nguyen, Kečstutis Karčiauskas |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
digital geometry
singular parameterization Logic 02 engineering and technology Isogeometric analysis Poisson distribution 01 natural sciences symbols.namesake 0202 electrical engineering electronic engineering information engineering Poisson’s equation Digital geometry Extraordinary points Singular parameterization G1 parameterization Applied mathematics 0101 mathematics Mathematical Physics Mathematics Algebra and Number Theory extraordinary points lcsh:Mathematics Mathematical analysis 020207 software engineering lcsh:QA1-939 Finite element method Quadrature (mathematics) 010101 applied mathematics isogeometric analysis symbols Geometry and Topology Poisson's equation Discrete differential geometry Analysis |
| Zdroj: | Axioms, Vol 3, Iss 2, Pp 280-299 (2014) Axioms; Volume 3; Issue 2; Pages: 280-299 Axioms, Basel : MDPI AG, 2014, Vol. 3, no. 2, p. 280-299 |
| ISSN: | 2075-1680 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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