Hierarchical Vector Bases for Pyramid Cells

Graglia, Roberto D.

doi:10.1109/iceaa49419.2022.9900017

Cited by 3 publications

(1 citation statement)

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“…Readers may find it helpful to review [5], [12] for a detailed introduction to the notation and other background information. Preliminar results of this work were presented in [23].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Divergence-Conforming Vector Bases for Pyramid Cells

Graglia

2023

IEEE Trans. Antennas Propagat.

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Divergence-conforming hierarchical vector bases for the pyramid consist of face-and volume-based functions obtained by a simple procedure that uses a new paradigm recently introduced by this author to produce pyramid bases. In order to define the bases' order, the procedure starts by mapping the pyramids into a cube of a new Cartesian space, which we call the grandparent space, where the basis functions and their divergences take on polynomial form. Then we get the face-based functions of zero polynomial order and the volumebased functions of the first order. Functions of arbitrarily high order are obtained by multiplying the vector functions of the lowest order by independent scalar polynomials of higher order. Our face-based functions conform to those of other differently shaped elements to allow the use of hybrid meshes, while the multiplicative construction technique generates right away the volume-based basis functions. The completeness of the bases is demonstrated and all the basis functions we obtain are suitably normalized; their expression involves orthogonal polynomials which are easy to implement and alleviate the loss of linear independence Index Terms -Electromagnetic fields, finite-element methods, higher order vector elements, pyramidal elements, numerical analysis.

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“…Readers may find it helpful to review [5], [12] for a detailed introduction to the notation and other background information. Preliminar results of this work were presented in [23].…”

Section: Introductionmentioning

confidence: 99%