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.
Bibliographical noteFunding Information:
The authors acknowledge the support of the German Research Foundation (DFG).
Copyright © 2019 Tech Science Press.
- Hourglass mode
- Nonlocal operator method
- Nonlocal operators
- Variational principle
ASJC Scopus subject areas
- Modelling and Simulation
- Mechanics of Materials
- Computer Science Applications
- Electrical and Electronic Engineering