A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem

Timon Rabczuk, Huilong Ren, Xiaoying Zhuang

Research output: Contribution to journalArticle

60 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)31-55
Number of pages25
JournalComputers, Materials and Continua
Volume59
Issue number1
DOIs
Publication statusPublished - 2019

Keywords

  • Hourglass mode
  • Nonlocal operator method
  • Nonlocal operators
  • Variational principle

ASJC Scopus subject areas

  • Biomaterials
  • Modelling and Simulation
  • Mechanics of Materials
  • Computer Science Applications
  • Electrical and Electronic Engineering

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