The dual primal finite element tearing and interconnecting method (FETI-DP) (Y. J. Li and J. M. Jin, IEEE Trans. Antennas Propagat., vol. 55, no. 10, pp. 2803-2810, 2007) is a stable domain decomposition method when dealing with subdomain conformal meshes for time-harmonic electromagnetic problems. Later, this method is further extended to nonconformal meshes (M. F. Xue and J. M. Jin, IEEE Trans. Antennas Propagat., vol. 60, no. 9, pp. 4291-4305, 2012). To the best of our knowledge, no matter the mesh is conformal or nonconformal, the existing FETI-DP algorithms are limited to the case with a conformal subdomain geometry, which means subdomain interfaces have a one-on-one correspondence. However, in some practical applications, we need to mesh different parts of the entire computational domain (denoted as regions in the following context) separately, and then decompose these separate meshes into subdomains independently. In this case, the connectivity between two subdomains across the region interfaces could be arbitrary; and the existing FETI-DP algorithms are no longer applicable.