A novel higher order large-domain hybrid computational electromagnetic technique based on the finite element method (FEM) and method of moments (MoM) is proposed for three-dimensional analysis of antennas and scatterers in the frequency domain. The geometry of the structure is modeled using generalized curved parametric hexahedral and quadrilateral elements of arbitrary geometrical orders. The fields and currents on elements are modeled using curl- and divergence-conforming hierarchical polynomial vector basis functions of arbitrary approximation orders, and the Galerkin method is used for testing. The elements can be as large as about two wavelengths in each dimension. As multiple MoM objects are possible in a global exterior region, the MoM part provides much greater modeling versatility and potential for applications, especially in antenna problems, than just as a boundary-integral closure to the FEM part. The examples demonstrate excellent accuracy, convergence, efficiency, and versatility of the new FEM-MoM technique, and very effective large-domain meshes that consist of a very small number of large flat and curved FEM and MoM elements, with p-refined field and current distributions of high approximation orders. The reduction in the number of unknowns is by two orders of magnitude when compared to available data for low-order FEM-MoM modeling.

An efficient and accurate large-domain higher order two-dimensional (2-D) Galerkin-type technique based on the finite-element method (FEM) is proposed for analysis of arbitrary electromagnetic waveguides. The geometry of a waveguide cross section is approximated by a mesh of large Lagrangian generalized curvilinear quadrilateral patches of arbitrary geometrical orders (large domains). The fields over the elements are approximated by a set of hierarchical 2-D polynomial curl-conforming vector basis functions of arbitrarily high field-approximation orders. When compared to the conventional small-domain 2-D FEM techniques, the large-domain technique requires considerably fewer unknowns for the same (or higher) accuracy and offers a significantly faster convergence when the number of unknowns is increased. A comparative analysis of solutions using p- and h-refinements shows that the p-refinement represents a better choice for higher accuracy with lesser computation cost. In addition to increasing the field-approximation orders, the geometrical orders of elements (where needed) should also be set high for the improved accuracy of the solution without subdividing the elements. However, in general, an arbitrarily high accuracy cannot be achieved by performing the p-refinement in arbitrarily coarse meshes alone; instead, a combined hp-refinement should be utilized in order to obtain an optimal modeling performance.

Occasionally, Hashimoto's thyroiditis (HT) and papillary thyroid carcinoma (PTC) share similar nuclear features. The current study aims to quantify the differences between the investigated specimens of HT-associated PTC versus the HT alone, to reduce the subjective experience of an observer, by the use of fractal parameters as well as gray-level co-occurrence matrix (GLCM) textural parameters. We have analyzed 250 segmented nuclei per group (n_n= 25 per patient andn_p= 10 patients per group) using the ImageJ software (NIH, Bethesda, MD, USA) as well as an in-house written code for the GLCM analysis. The mean values of parameters were calculated for each patient. The results demonstrated that the malignant cells from the HT-associated PTC specimens showed lower chromatin fractal dimension (p= 0.0321) and higher lacunarity (p= 0.0038) compared with the corresponding cells from the HT specimens. Also, there was a statistically significant difference between the investigated specimens, in the contrast, correlation, angular second moment, and homogeneity, of the GLCM corresponding to the visual texture of follicular cell chromatin. The differences in chromatin fractal and GLCM parameters could be integrated with other diagnostic methods for the improved evaluation of distinctive features of the HT-associated PTC versus the HT in cytology and surgical pathology specimens.