Details
| Original language | English |
|---|---|
| Article number | 113132 |
| Number of pages | 27 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 367 |
| Early online date | 27 May 2020 |
| Publication status | Published - 1 Aug 2020 |
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.
Keywords
- Higher order nonlocal operators, Operator energy functional, PDEs, Strong form
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 367, 113132, 01.08.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A higher order nonlocal operator method for solving partial differential equations
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Rabczuk, Timon
N1 - Funding Information: The supports from National Basic Research Program of China (973 Program: 2011CB013800 ) and NSFC ( 51474157 ), the Ministry of Science and Technology of China (Grant No. SLDRCE14-B-28 , SLDRCE14-B-31 ) are acknowledged.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - 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.
AB - 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.
KW - Higher order nonlocal operators
KW - Operator energy functional
KW - PDEs
KW - Strong form
UR - http://www.scopus.com/inward/record.url?scp=85085257298&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1905.02809
DO - 10.48550/arXiv.1905.02809
M3 - Article
VL - 367
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 113132
ER -