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Orthogonal Hierarchical NÉdÉlec Elements
2008 Edition, Volume 44, June 1, 2008 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

An orthogonalization procedure for a set of high-order hierarchical (curl)-conforming basis functions or tangential vector elements which retains the span of the Nedelec space is proposed as an alternative to the Gram-Schmidt procedure which cannot be used without compromising...

Hierarchical universal matrices for sensitivity analysis by curvilinear finite elements
2018 Edition, March 1, 2018 - Applied Computational Electromagnetics Society (ACES)

A new method for calculating the geometric sensitivities of curvilinear finite elements is presented. Approximating the relevant metric tensors by hierarchical orthogonal polynomials enables the sensitivity matrices to be integrated analytically. The resulting numerical method...

Attributed Graph Grammar for floor plan analysis
2015 Edition, August 1, 2015 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

In this paper, we propose the use of an Attributed Graph Grammar as unique framework to model and recognize the structure of floor plans. This grammar represents a building as a hierarchical composition of structurally and semantically related elements, where common representations...

FEM analysis of dielectric loaded waveguides with additive hierarchical singular vector elements
2014 Edition, July 1, 2014 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Summary form only given. For problems with smooth surfaces or other regular features, high order hierarchical bases successfully improve accuracy and efficiency. However, for geometries with edges or corners where unbounded fields or other singular types of behavior occur, special bases that...

Spatially Large-Domain and Temporally Entire-Domain Electric-Field Integral Equation Method of Moments for 3-D Scattering Analysis in Time Domain
2015 Edition, Volume 63, June 1, 2015 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

A novel spatially large-domain and temporally entire-domain method of moments (MoM) is proposed for surface integral equation (SIE) modeling of 3-D conducting scatterers in the time domain (TD). The method uses higher order curved Lagrange interpolation-generalized quadrilateral geometrical...

Hierarchical Divergence-Conforming Nédélec Elements for Volumetric Cells
2012 Edition, Volume 60, November 1, 2012 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

A new family of hierarchical divergence-conforming vector bases is proposed for tetrahedral, prism and brick cells. These functions span the divergence-conforming reduced-curl spaces of Nédélec. The bases are constructed from orthogonal scalar polynomials to enhance their...

Singular hierarchical vector elements of the additive kind for triangular meshes
2013 Edition, July 1, 2013 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Summary form only given. New hierarchical vector elements of arbitrary polynomial order were recently derived in [(1) R. D. Graglia, A.F. Peterson, F.P. Andriulli, "Curl-conforming hierarchical vector bases for triangles and tetrahedra," IEEE TAP, vol. 59, no. 3, pp. 950-959,...

Hierarchical Curl-Conforming Nédélec Elements for Triangular-Prism Cells
2012 Edition, Volume 60, July 1, 2012 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

New curl-conforming hierarchical vector basis functions are developed for triangular-prism cells. These bases are constructed by taking the product of base vectors with scalar orthogonal polynomials and are shown to maintain linear independence as their polynomial order is increased....

Marching-on-in-degree solver of time domain integral equation based on near-orthogonal higher order hierarchical basis functions
2012 Edition, Volume 2, May 1, 2012 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

In this paper, the time domain integral equation is solved by marching-on-in-degree method with near-orthogonal higher order hierarchical Legendre basis as spatial basis functions and causal weighted Laguerre polynomials as temporal basis functions. In the traditional...

Systematic construction and performance comparison for higher order hierarchical tetrahedral vector elements
2010 Edition, October 1, 2010 - IEEE - Institute of Electrical and Electronics Engineers, Inc.

Nedelec's functional spaces of H 1 (curl) hierarchical tetrahedral vector elements are analyzed systematically by using the method combined Nedelec constraints and complete polynomials. The relations between various vector elements and the functional spaces are validated...

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