A novel implementation of symmetric boundary condition in harmonic and transient analysis of electromagnetic wave propagation

While doing electromagnetic analysis using FEM, using symmetry, if exists will minimize the computational cost. Through the physical problem definition, it is possible to determine if symmetry exists about one plane for particular electromagnetic problems. The adoption of suitable symmetry boundary conditions can help to minimize the computing domain for these types of problems. But for electromagnetic analysis in potential formulation it is not very straight forward to implement the symmetric boundary condition. In the present work, a novel approach of implementation of symmetry boundary condition in potential formulation within nodal framework has been demonstrated. Also, it is implemented to various electromagnetic harmonic and transient problems. These problems include various domains such as conducting and dielectric sphere, cube with conducting walls and ellipsoid. A significant reduction in computational cost is achieved using the proposed method.Comment: 16 Pages, !9 Figures, 6 Table

An amplitude finite element formulation for electromagnetic radiation and scattering

Electromagnetic radiation and scattering in an exterior domain within the context of a finite element method has traditionally involved imposing a suitable absorbing boundary condition on the truncation boundary of the numerical domain to inhibit reflection from it. In this work, based on the Wilcox asymptotic expansion of the electric far-field, we propose an amplitude formulation within the framework of the nodal finite element method, whereby the highly oscillatory radial part of the field is separated out a-priori so that the standard Lagrange interpolation functions that are used have to capture a relatively gently varying function. Since these elements can be used in the immediate vicinity of the radiator or scatterer (with few exceptions which we enumerate), it is more effective compared to methods that impose absorbing boundary conditions at the truncation boundary, especially for high-frequency problems. The proposed method is based on the standard Galerkin finite element formulation, and uses standard Lagrange interpolation functions, standard Gaussian quadrature and the same degrees of freedom as a conventional formulation. We show the effectiveness of the proposed formulation on a wide variety of radiation and scattering problems involving both conducting and dielectric bodies, and involving both convex and non-convex domains with sharp corners. (C) 2016 Elsevier Ltd. All rights reserved