The fictitious domain method and homotopy as a new alternative for multidimensional partial differential equations in domains of any shape
UDC 517.9; 519.63 The ideas of the fictitious domain method and homotopy are combined with an aim to reduce the solution of boundary-value problems for multidimensional partial differential equations (PDE) in domains of any shape to an exponentially convergent sequence of PDEs in a parallelepiped (i...
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| Datum: | 2020 |
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| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1101 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.9; 519.63
The ideas of the fictitious domain method and homotopy are combined with an aim to reduce the solution of boundary-value problems for multidimensional partial differential equations (PDE) in domains of any shape to an exponentially convergent sequence of PDEs in a parallelepiped (in a rectangle, in the 2D case). This allows us to reduce the computational costs due to the elimination of the necessity of triangulation of the domain by a grid with $N$ inner nodes (e.g., the Delaunay algorithm in the 2D case requires ${\mathcal {O}}(N \log{N})$ operations). |
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