Timon Rabczuk1,2,*, Huilong Ren3, Xiaoying Zhuang4,5
CMC-Computers, Materials & Continua, Vol.59, No.1, pp. 31-55, 2019, DOI:10.32604/cmc.2019.04567
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… More >
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