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A new numerical discretization of the complex frequency shifted‐perfectly matched layer (CFS‐PML) is presented for truncation of open domains. This discretization is based on the theory of discrete differential forms applied to electromagnetism, which guarantees both the simplification of the algorithms and a more elegant formulation of expression. The curl Maxwell's equations are solved in time domain in terms of electric e magnetic fields. The Ampere‐Maxwell law with, the constitutive relations included through the Hodge operator, is discretized in space by applying the Galerkin method. Conversely, the Faraday law is represented by topological relations via incidence matrix. The time domain discretization uses the leap‐frog scheme with a recursive convolution inside PML region. Two examples are shown, the first one to validate the CFS‐PML procedure and the second one to solve a typical ground penetrating radar scenario which include a lossy media. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:351–357, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27298

To solve wave propagation problems over large domains composed by different media, many authors use the generalized finite element method (GFEM) with a geometrically conforming partition and plane wave enrichment.Such analysis is often accomplished by decomposing the entire domain into several subdomains and performing the analysis individually on each one. Then, the global analysis can be realized by using Lagrange multipliers to ensure the interface constraints. In this article, the GFEM with plane wave enrichment is extended to nonconforming discrete cases where the interface between the media can be handled as piecewise linear segments. Results for problems for which the analytical solution is known are presented to demonstrate the efficiency of the proposed technique. The convergence of the method is also presented as a function of the number of plane wave directions. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2709–2716, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27166

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