A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem

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.

The original publication is available at https://doi.org/10.32604/cmc.2019.04567

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The work is done by the team  Prof. Xiaoying Zhuang


[1] Kamensky, David, et al. Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines. Computer methods in applied mechanics and engineering 314 (2017): 408-472. 

[2] Ren, Huilong, Xiaoying Zhuang, and Timon Rabczuk. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering 318 (2017): 762-782.