Name
Title | ||
|---|---|---|
Elliptic grid generation techniques in the framework of isogeometric analysis applications. |
Abstract | ||
|---|---|---|
The generation of an analysis-suitable computational grid from a description of no more than its boundaries is a common problem in numerical analysis. Most classical meshing techniques for finite-volume, finite-difference or finite-element applications such as the Advancing Front Method (Schöberl, 1997), Delaunay Triangulation (Triangle, 1996) and elliptic or hyperbolic meshing schemes (Thompson et al., 1998) operate with linear or multi-linear but straight-sided elements for the generation of structured and unstructured meshes, respectively, whereas the generation of high-quality curved meshes is still considered a major challenge. A recent development is the introduction of Isogeometric Analysis (IgA) (Hughes et al., 2005), which can be considered as a natural high-order generalisation of the finite-element method. A description of the geometry Ω¯ is accomplished via a mapping operator x:Ωˆ→Ω that maps the unit hypercube in Rn onto an approximation Ω of Ω¯ utilizing a linear combination of higher-order spline functions. The numerical simulation is then carried out in the computational domain Ωˆ via a ‘pull back’ using the mapping operator x. The advantage is that the flexibility of higher-order spline-functions usually allows for an accurate description of Ω¯ with much fewer elements which can significantly reduce the computational effort required for this step compared to traditional low-order methods. Furthermore, an analytical description of the geometry can be turned back into a traditional (structured or unstructured) grid by performing a large number of function evaluations in x. This can, for instance, be utilized for local refinement without the need for remeshing. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.cagd.2018.03.023 | Computer Aided Geometric Design |
Field | DocType | Volume |
Linear combination,Topology,Nonlinear system,Polygon mesh,Isogeometric analysis,Numerical analysis,Mesh generation,Mathematics,Grid,Delaunay triangulation | Journal | 65 |
ISSN | Citations | PageRank |
0167-8396 | 0 | 0.34 |
References | Authors | |
10 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. Hinz | 1 | 0 | 0.34 |
| Matthias Möller | 2 | 1 | 4.08 |
| Cornelis Vuik | 3 | 0 | 0.34 |