A Moving Mesh Isogeometric Method Based on Harmonic Maps
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913642662854656 |
|---|---|
| author | Wang, Tao Meng, Xucheng Zhang, Ran Hu, Guanghui |
| author_facet | Wang, Tao Meng, Xucheng Zhang, Ran Hu, Guanghui |
| contents | Although the isogeometric analysis has shown its great potential in achieving highly accurate numerical solutions of partial differential equations, its efficiency is the main factor making the method more competitive in practical simulations. In this paper, an integration of isogeometric analysis and a moving mesh method is proposed, providing a competitive approach to resolve the efficiency issue. Focusing on the Poisson equation, the implementation of the algorithm and related numerical analysis are presented in detail, including the numerical discretization of the governing equation utilizing isogeometric analysis, and a mesh redistribution technique developed via harmonic maps. It is found that the isogeometric analysis brings attractive features in the realization of moving mesh method, such as it provides an accurate expression for moving direction of mesh nodes, and allows for more choices for constructing monitor functions. Through a series of numerical experiments, the effectiveness of the proposed method is successfully validated and the potential of the method towards the practical application is also well presented with the simulation of a helium atom in Kohn--Sham density functional theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Moving Mesh Isogeometric Method Based on Harmonic Maps Wang, Tao Meng, Xucheng Zhang, Ran Hu, Guanghui Numerical Analysis Although the isogeometric analysis has shown its great potential in achieving highly accurate numerical solutions of partial differential equations, its efficiency is the main factor making the method more competitive in practical simulations. In this paper, an integration of isogeometric analysis and a moving mesh method is proposed, providing a competitive approach to resolve the efficiency issue. Focusing on the Poisson equation, the implementation of the algorithm and related numerical analysis are presented in detail, including the numerical discretization of the governing equation utilizing isogeometric analysis, and a mesh redistribution technique developed via harmonic maps. It is found that the isogeometric analysis brings attractive features in the realization of moving mesh method, such as it provides an accurate expression for moving direction of mesh nodes, and allows for more choices for constructing monitor functions. Through a series of numerical experiments, the effectiveness of the proposed method is successfully validated and the potential of the method towards the practical application is also well presented with the simulation of a helium atom in Kohn--Sham density functional theory. |
| title | A Moving Mesh Isogeometric Method Based on Harmonic Maps |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.05118 |