Accuracy in EM Fields Calculations Using a Combined FE-IE Approach
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FE-IE hybrid finite element-integral equation EM f↗
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Analytical evaluation of a surface integral expressing the coupling between interior and exterior volumes in a FE-IE approach
Recently an approach which combines the finite element technique and an integral equation to determine the fields scattered by inhomogeneous bodies of complicated shape has been proposed. Basically, a mathematical surface which encloses the scatterers is introduced, thus dividing the space into an interior and an exterior volume, in which the finite element technique and an integral equation for EM scattering, respectively, are applied. The integral equation is set up for the tangential components of the fields at the surface, while the interior volume the unknowns are the total fields. Continuity of the tangential fields at the boundary, as required by Maxwell's equations, is imposed, thus coupling the two methods to obtain a consistent solution. The coupling term is expressed by a surface integral formed by the dot product of a FE basis function and an IE testing function, or viceversa. By choosing the boundary to be a surface of revolution and by making a convenient selection of IE basis (testing) functions, it is possible to evaluate the integrals analytically on surfaces such as curved triangles, curved quadrilaterals and curved pentagons. We will illustrate the salient steps involved in setting up and carrying out these integrals and discuss what class of basis (testing) functions and analytic surfaces of revolution they are applicable to. Analytic calculations offer the advantage of better accuracy than purely numerical ones, and, when combined with them, often shed light on issues of numerical convergence and limiting values. Furthermore, they may reduce computation time and storage requirements.
Zuffada, C.↗
Performing spectroscopic and specific heat studies of improper ferroelectrics
The results of infrared measurements on Ni-Br, Cu-Cl, and Fe-I boracite improper ferroelectrics and far infrared measurements of Ni-Br boracite are presented. The boracites have the general formula X3B7O3Y, where X = divalent metal and Y = halogen. They undergo a first order phase transition from a high temperature paraelectric phase with cubic symmetry to a ferroelectric phase with orthorhombic symmetry. The boracites are "improper ferroelectrics" since the spontaneous polarization is not the primary order parameter in the cubic-orthorhombic phase transition. Current understanding of these materials is that the primary order parameter is associated with a doubly degenerate zone-boundary phonon in the cubic phase. The degenerate critical modes become homogeneous and split into the A sub 1 and A sub 2 modes in the orthorhombic phase, doubling the volume of the primitive cell. An harmonic coupling between the softing A sub 1 and a low frequency A sub 1 optic mode induces a spontaneous polarization as a secondary effect in the ferroelectric phase. This secondary non-critical nature of the ferroelectric mode earns these materials the "improper" title and is responsible for their unique properties and high figure of merit in detector use.
Coleman, L. B.↗
Recalibration of Mount Wilson Doppler measurements (Research note)
The dispersion calibration of spectroscopic velocity measurements made with the 150-ft tower telescope at Mt. Wilson Observatory is revised upward by 0.55 percent on the basis of observations of the six lines of comparable shape and equivalent width nearest the 5250.2-A line of Fe-I used in the solar Doppler rate measurements. The dispersion results are presented in a graph, and the superiority of the Kitt Peak wavelength tables (Pierce and Breckenridge, 1973) over those of Moore et al. (1966) is demonstrated. As a result of the recalibration, all recent spectroscopic velocities from this telescope must be revised downward by 0.55 percent.
Snodgrass, H. B.↗
An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems
It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.
Cwik, T.↗