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Waveguides are structures consisting of geometrically identical subdomains, usually called periodic cells which have many practical applications, for example, optical Communications, filters, lasers, and microwaves. Finite element based approaches for infinite periodic structures have one fundamental restriction. The finite element mesh on opposite sides of the cell must be exactly the same, i.e., a periodic mesh. In this paper, we consider a novel finite element meshing method for calculation of waveguide band structures. In particular, we propose a simple mapping scheme to generate periodic mesh. We first map the periodic cell to a closed domain such that the periodic cell are glued together in the new domain. Then we can apply mesh generation schemes to obtain a regular triangular mesh. This mesh is mapped back to the periodic cell such that the nodes and edges on the periodic boundaries are matched.