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Algorithmic Implementation of a Hybrid 2D Finite Element - Mode Matching Method Based on Nested Function Spaces

Abstract:

This work reports an algorithmic implementation of a hybrid finite element (FE) - mode matching technique based on the concept of nested 2D FE function spaces, suited to analyze waveguide components with diverse geometries as for instance transformers or polarizers for antenna feeds. Thanks to this technique, the inner cross product matrix in the mode matching method is readily built from precomputed FE matrices, which are already available from the mode computation in irregularly shaped cross-sections. Thus, this work focuses on the implementation of this technique such that critical steps are carried out in an efficient way (i.e. sparse matrix-vector products, vector-vector dot products, etc.). To that effect, a very powerful and flexible FE open source computing platform, namely FEniCS, along with its high-level Python interface, has been used.