Finite Element Analysis of All Modes in Cavities with Circular Symmetry

The Origin of Spurious Solutions in Computational Electromagnetics

“…The curl-curl equations are derived from the first-order ment method, (see, e.g., Cendes and Silvester [7], Bird [3], Ikeuchi et al [20], Mabaya et al [35], Davies et al [12], Maxwell curl equations by applying the curl operator.…”

Finite elements with divergence-free shape function and the application to inhomogeneously-loaded waveguide analysis

“…Considering a metallic-walled waveguide with closed cross-section n, the source-free Maxwell's equations with time dependence of exp(jrot) being implied are given by V x E =-jrollollrH V x H =jrofoerE (1) ( 2) where ro is the angular frequency, EO and Ilo are the permittivity and permeability of free space, respectively, and Er and Ilr are the corresponding relative material properties. At the interface between two contiguous media i and j, the following conditions must be satisfied:…”

“…Several methods have been proposed to suppress these spurious solutions. One of the earliest proposal to identify these spurious modes, made by Davies [2] was to include the square of the proposes the use of the shape functions which does not need any pre-fixing but is inherently divergence-free. This means that the present shape functions accommodate straightforwardly the zero divergence of the field in the formulation in an explicit way and get rid of the spurious solutions resulting from the non-compliance with divergence-free condition.…”

Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements

“…Unfortunately, after some success with scalar 2D models, more complicated ones, (no matter whether finite difference or finite element based) were often affected by extraneous solutions. In particular, some of the first finite element models of resonant cavities were totally unreliable as a consequence of the presence of the so-called spurious modes mixed with physical ones and spread over the whole numerically calculated spectrum [15,18,22]. Some years later, Nedelec introduced a family of elements [29] well suited to the study of 3D vector problems involving electromagnetic fields.…”