Abstract
The isogeometric Nyström method is presented in this paper. The important features of the method are: it allows the analysis of domains described by many different geometry descriptions in computer aided geometric design and it requires only pointwise function evaluations similar to isogeometric collocation methods. The analysis of the computational domain is carried out by means of boundary integral equations, therefore a boundary representation only is required. The method is thoroughly integrated into the isogeometric framework. For example, the regularization of the singular integrals arising is performed with local correction and also the interpolation of the pointwise results is carried out by means of Bézier elements. The isogeometric Nyström method is applied to practical problems solved by the Laplace and the Lamé-Navier equation. Numerical tests show a higher order convergence in two and three dimensions. It is concluded that the approach presented provides a simple and flexible alternative to the methods currently used for solving boundary integral equations, although it does have some limitations.
| Originalsprache | englisch |
|---|---|
| Seiten (von - bis) | 212-237 |
| Seitenumfang | 26 |
| Fachzeitschrift | Computer Methods in Applied Mechanics and Engineering |
| Jahrgang | 308 |
| DOIs | |
| Publikationsstatus | Veröffentlicht - 15 Aug 2016 |
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ASJC Scopus subject areas
- !!Computational Mechanics
- !!Mechanics of Materials
- !!Mechanical Engineering
- !!Physics and Astronomy(all)
- !!Computer Science Applications
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The isogeometric Nyström method. / Zechner, Jürgen; Marussig, Benjamin; Beer, Gernot; Fries, Thomas Peter.
in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 308, 15.08.2016, S. 212-237.Publikation: Beitrag in einer Fachzeitschrift › Artikel › Forschung › Begutachtung
}
TY - JOUR
T1 - The isogeometric Nyström method
AU - Zechner, Jürgen
AU - Marussig, Benjamin
AU - Beer, Gernot
AU - Fries, Thomas Peter
PY - 2016/8/15
Y1 - 2016/8/15
N2 - The isogeometric Nyström method is presented in this paper. The important features of the method are: it allows the analysis of domains described by many different geometry descriptions in computer aided geometric design and it requires only pointwise function evaluations similar to isogeometric collocation methods. The analysis of the computational domain is carried out by means of boundary integral equations, therefore a boundary representation only is required. The method is thoroughly integrated into the isogeometric framework. For example, the regularization of the singular integrals arising is performed with local correction and also the interpolation of the pointwise results is carried out by means of Bézier elements. The isogeometric Nyström method is applied to practical problems solved by the Laplace and the Lamé-Navier equation. Numerical tests show a higher order convergence in two and three dimensions. It is concluded that the approach presented provides a simple and flexible alternative to the methods currently used for solving boundary integral equations, although it does have some limitations.
AB - The isogeometric Nyström method is presented in this paper. The important features of the method are: it allows the analysis of domains described by many different geometry descriptions in computer aided geometric design and it requires only pointwise function evaluations similar to isogeometric collocation methods. The analysis of the computational domain is carried out by means of boundary integral equations, therefore a boundary representation only is required. The method is thoroughly integrated into the isogeometric framework. For example, the regularization of the singular integrals arising is performed with local correction and also the interpolation of the pointwise results is carried out by means of Bézier elements. The isogeometric Nyström method is applied to practical problems solved by the Laplace and the Lamé-Navier equation. Numerical tests show a higher order convergence in two and three dimensions. It is concluded that the approach presented provides a simple and flexible alternative to the methods currently used for solving boundary integral equations, although it does have some limitations.
KW - Boundary integral equation
KW - Collocation
KW - Isogeometric analysis
KW - Local refinement
UR - http://www.scopus.com/inward/record.url?scp=84977074118&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2016.03.043
DO - 10.1016/j.cma.2016.03.043
M3 - Article
VL - 308
SP - 212
EP - 237
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -