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

• 作者: Huilong Ren Timon Rabczuk Xiaoying Zhuang
• 来源期刊: 计算机、材料和连续体(英文)
• 学科: 数学
• 关键词: NONLOCAL operator method VARIATIONAL principle NONLOCAL OPERATORS HOURGLASS mode
• 年，卷（期）: 2019,（4）
• 页码范围: 31-55
• 页数: 25页
• 分类号: O17

摘要

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 zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.