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

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Rabczuk, T.; Ren, H.; Zhuang, X.: A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem. In: Computers, Materials & Continua 59 (2019), Nr. 1, S. 31-55. DOI: https://doi.org/10.32604/cmc.2019.04567

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Sum total of downloads: 85

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.
License of this version: CC BY 4.0
Document Type: article
Publishing status: publishedVersion
Issue Date: 2019
Appears in Collections:Fakultät für Maschinenbau

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pos. country downloads
total perc.
1 image of flag of Germany Germany 32 37.65%
2 image of flag of China China 18 21.18%
3 image of flag of United States United States 10 11.76%
4 image of flag of Iran, Islamic Republic of Iran, Islamic Republic of 9 10.59%
5 image of flag of Australia Australia 5 5.88%
6 image of flag of Malaysia Malaysia 3 3.53%
7 image of flag of India India 2 2.35%
8 image of flag of Italy Italy 1 1.18%
9 image of flag of Hong Kong Hong Kong 1 1.18%
10 image of flag of United Kingdom United Kingdom 1 1.18%
    other countries 3 3.53%

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