I am not sure if it's free but Hypermesh will be a good choice

Good topic- Following

We use Netgen with the Python frontend https://ngsolve.org. I would also checkout gmsh. https://gmsh.info

thanks dear Mohit Goswami , but i don't think this mesh generator is free

Thank you dear Peter B Monk, have you ever used these two software to create periodic meshes?

You can try to use Gambit software.

Hi Yu Jiang, thank you for your answer.

have you already used this software to create periodic structures? If so, are you creating them by symmetry of half, quarter, eighth or by translating the border surfaces?

Salome is a good open-source meshing tool which can help you create structured and unstructured meshes. You can create projection of a mapped mesh from one of the periodic face to the other so that the nodes are duplicated on both the faces. I use Salome for meshing purposes for creating all kinds of complicated meshes.

I used netgen (free) regularly last year to compute 3D Maxwell on biperiodic gratings. It will produce periodic meshes in 2D and 3D.

Dear Peter B Monk, thank you very much for your reply.