Details
| Original language | English |
|---|---|
| Pages (from-to) | 31-55 |
| Number of pages | 25 |
| Journal | Computers, Materials and Continua |
| Volume | 59 |
| Issue number | 1 |
| Publication status | Published - 2019 |
Abstract
A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity, which is necessary for the eigenvalue analysis such as the waveguide problem. The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields. The governing equations are converted into nonlocal integral form. An hourglass energy functional is introduced for the elimination of zero-energy modes. Finally, the proposed method is validated by testing three classical benchmark problems.
Keywords
- Hourglass mode, Nonlocal operator method, Nonlocal operators, Variational principle
ASJC Scopus subject areas
- Materials Science(all)
- Biomaterials
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Mechanics of Materials
- Computer Science(all)
- Computer Science Applications
- Engineering(all)
- Electrical and Electronic Engineering
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In: Computers, Materials and Continua, Vol. 59, No. 1, 2019, p. 31-55.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem
AU - Rabczuk, Timon
AU - Ren, Huilong
AU - Zhuang, Xiaoying
N1 - Funding information: The authors acknowledge the support of the German Research Foundation (DFG).
PY - 2019
Y1 - 2019
N2 - A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity, which is necessary for the eigenvalue analysis such as the waveguide problem. The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields. The governing equations are converted into nonlocal integral form. An hourglass energy functional is introduced for the elimination of zero-energy modes. Finally, the proposed method is validated by testing three classical benchmark problems.
AB - A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity, which is necessary for the eigenvalue analysis such as the waveguide problem. The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields. The governing equations are converted into nonlocal integral form. An hourglass energy functional is introduced for the elimination of zero-energy modes. Finally, the proposed method is validated by testing three classical benchmark problems.
KW - Hourglass mode
KW - Nonlocal operator method
KW - Nonlocal operators
KW - Variational principle
UR - http://www.scopus.com/inward/record.url?scp=85064858488&partnerID=8YFLogxK
U2 - 10.32604/cmc.2019.04567
DO - 10.32604/cmc.2019.04567
M3 - Article
AN - SCOPUS:85064858488
VL - 59
SP - 31
EP - 55
JO - Computers, Materials and Continua
JF - Computers, Materials and Continua
SN - 1546-2218
IS - 1
ER -