Handling material discontinuities in a nonconforming generalized finite element method enriched by plane waves. Part II. Curvilinear interfaces.

ABSTRACT In Part I (W. G. Facco et al., Microwave and Optical Technology Letters 54 (2012) 2709-2716), we introduced the q-version of the nonconforming generalized finite element method (NC-GFEM) for the Helmholtz equation where the interface between the media can be handled as piecewise linear segments. Here we continue the development of the NC-GFEM for Helmholtz where the interface between the media can be handled as piecewise curvilinear. We address: (a) a new scheme of integration to evaluate the integral along the interfaces and (b) the mortar element method (MEM) as a substitute for the Lagrange multipliers. The MEM has the advantage of generating sparse and positive definite systems. Various numerical aspects affecting the NC-GFEM efficiency are analyzed by solving a two-dimensional scattering problem. The convergence of the method is also presented as a function of the number of plane wave directions. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1913-1919, 2014 [ABSTRACT FROM AUTHOR]