Numerical quadrature for Gregory quads

Jun Zhou; Pieter J. Barendrecht; Jiri Kosinka; Michael Bartoň

doi:10.1016/j.amc.2023.128051

Numerical quadrature for Gregory quads

Jun Zhou, Pieter J. Barendrecht, Jiri Kosinka^*, Michael Bartoň

^*Corresponding author for this work

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Abstract

We investigate quadrature rules in the context of quadrilateral Gregory patches, in short Gregory quads. We provide numerical and where possible symbolic quadrature rules for the space spanned by the twenty polynomial/rational functions associated with Gregory quads, as well as the derived spaces including derivatives, products, and products of derivatives of these functions. This opens up the possibility for a wider adoption of Gregory quads in numerical simulations.

Original language	English
Article number	128051
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	453
DOIs	https://doi.org/10.1016/j.amc.2023.128051
Publication status	Published - 15-Sept-2023

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title = "Numerical quadrature for Gregory quads",

abstract = "We investigate quadrature rules in the context of quadrilateral Gregory patches, in short Gregory quads. We provide numerical and where possible symbolic quadrature rules for the space spanned by the twenty polynomial/rational functions associated with Gregory quads, as well as the derived spaces including derivatives, products, and products of derivatives of these functions. This opens up the possibility for a wider adoption of Gregory quads in numerical simulations.",

author = "Jun Zhou and Barendrecht, {Pieter J.} and Jiri Kosinka and Michael Barto{\v n}",

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T1 - Numerical quadrature for Gregory quads

AU - Zhou, Jun

AU - Barendrecht, Pieter J.

AU - Kosinka, Jiri

AU - Bartoň, Michael

PY - 2023/9/15

Y1 - 2023/9/15

N2 - We investigate quadrature rules in the context of quadrilateral Gregory patches, in short Gregory quads. We provide numerical and where possible symbolic quadrature rules for the space spanned by the twenty polynomial/rational functions associated with Gregory quads, as well as the derived spaces including derivatives, products, and products of derivatives of these functions. This opens up the possibility for a wider adoption of Gregory quads in numerical simulations.

AB - We investigate quadrature rules in the context of quadrilateral Gregory patches, in short Gregory quads. We provide numerical and where possible symbolic quadrature rules for the space spanned by the twenty polynomial/rational functions associated with Gregory quads, as well as the derived spaces including derivatives, products, and products of derivatives of these functions. This opens up the possibility for a wider adoption of Gregory quads in numerical simulations.

U2 - 10.1016/j.amc.2023.128051

DO - 10.1016/j.amc.2023.128051

M3 - Article

SN - 0096-3003

VL - 453

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 128051

ER -

Numerical quadrature for Gregory quads

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