A higher order nonlocal operator method for solving partial differential equations
- verfasst von
- Huilong Ren, Xiaoying Zhuang, Timon Rabczuk
- Abstract
A higher order nonlocal operator method for the solution of boundary value problems is developed. The proposed higher order nonlocal operator brings several advantages as compared to the original nonlocal operator method (Ren et al., 2020) which only ensures first-order convergence. Furthermore, it can be applied to directly and efficiently obtain all partial derivatives of higher orders simultaneously without the need of using shape functions. Only the functionals based on the nonlocal operators (termed as operator functional) are needed to obtain the final discrete system of equations, which significantly facilitates the implementation. Several numerical examples are presented to show the effectiveness and accuracy of the proposed higher order nonlocal operator method including the solution of the Poisson equation in 2–5 dimensional space, Kirchhoff and von Kármán plate problems, incompressible elastic materials as well as phase field modeling of fracture.
- Organisationseinheit(en)
-
Institut für Kontinuumsmechanik
- Externe Organisation(en)
-
Bauhaus-Universität Weimar
Tongji University
Ton Duc Thang University
- Typ
- Artikel
- Journal
- Computer Methods in Applied Mechanics and Engineering
- Band
- 367
- Anzahl der Seiten
- 27
- ISSN
- 0045-7825
- Publikationsdatum
- 01.08.2020
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Physik und Astronomie (insg.), Angewandte Informatik
- Elektronische Version(en)
-
https://doi.org/10.48550/arXiv.1905.02809 (Zugang:
Offen)
https://doi.org/10.1016/j.cma.2020.113132 (Zugang: Geschlossen)
