High‐order cubature rules for tetrahedra

Jaśkowiec, Jan; Sukumar, N.

doi:10.1002/nme.6313

Title: High‐order cubature rules for tetrahedra

Authors:

^[1];

^[2]

Faculty of Civil Engineering Cracow University of Technology Cracow Poland
Department of Civil and Environmental Engineering University of California Davis California

Publication Date:: 2020-01-29

Sponsoring Org.:: USDOE

OSTI Identifier:: 1596161

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: International Journal for Numerical Methods in Engineering

Additional Journal Information:: Journal Name: International Journal for Numerical Methods in Engineering Journal Volume: 121 Journal Issue: 11; Journal ID: ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)

Country of Publication:: United Kingdom

Language:: English

Citation Formats


                    Jaśkowiec, Jan, and Sukumar, N. High‐order cubature rules for tetrahedra.  United Kingdom: N. p., 2020. 
Web.  doi:10.1002/nme.6313.

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                    Jaśkowiec, Jan, & Sukumar, N. High‐order cubature rules for tetrahedra.  United Kingdom.  https://doi.org/10.1002/nme.6313

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                    Jaśkowiec, Jan, and Sukumar, N. Wed .  
"High‐order cubature rules for tetrahedra".  United Kingdom.  https://doi.org/10.1002/nme.6313.

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@article{osti_1596161,

  title        = {High‐order cubature rules for tetrahedra},

  author       = {Jaśkowiec, Jan and Sukumar, N.},

  abstractNote = {},

  doi          = {10.1002/nme.6313},

  journal      = {International Journal for Numerical Methods in Engineering},

  number       = 11,

  volume       = 121,

  place        = {United Kingdom},

  year         = {2020},

  month        = {1}

}

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Works referenced in this record:

Numerical integration on a tetrahedron
journal, June 1981

Hillion, P.
Calcolo, Vol. 18, Issue 2
DOI: 10.1007/BF02576492

Symmetric Quadrature Formulae for Simplexes
journal, January 1970

Silvester, P.
Mathematics of Computation, Vol. 24, Issue 109
DOI: 10.2307/2004880

New computationally efficient quadrature formulas for triangular prism elements
journal, March 2013

Kubatko, Ethan J.; Yeager, Benjamin A.; Maggi, Ashley L.
Computers & Fluids, Vol. 73
DOI: 10.1016/j.compfluid.2013.01.002

Invariant Integration Formulas for the n -Simplex by Combinatorial Methods
journal, April 1978

Grundmann, Axel; Möller, H. M.
SIAM Journal on Numerical Analysis, Vol. 15, Issue 2
DOI: 10.1137/0715019

Moderate Degree Symmetric Quadrature Rules for the Triangle
journal, January 1975

Lyness, J. N.; Jespersen, D.
IMA Journal of Applied Mathematics, Vol. 15, Issue 1
DOI: 10.1093/imamat/15.1.19

On the identification of symmetric quadrature rules for finite element methods
journal, May 2015

Witherden, F. D.; Vincent, P. E.
Computers & Mathematics with Applications, Vol. 69, Issue 10
DOI: 10.1016/j.camwa.2015.03.017

p-FEMs in biomechanics: Bones and arteries
journal, December 2012

Yosibash, Zohar
Computer Methods in Applied Mechanics and Engineering, Vol. 249-252
DOI: 10.1016/j.cma.2012.09.006

Some criteria for numerically integrated matrices and quadrature formulas for triangles
journal, January 1978

Laursen, M. E.; Gellert, M.
International Journal for Numerical Methods in Engineering, Vol. 12, Issue 1
DOI: 10.1002/nme.1620120107

Moderate-degree tetrahedral quadrature formulas
journal, May 1986

Keast, Patrick
Computer Methods in Applied Mechanics and Engineering, Vol. 55, Issue 3
DOI: 10.1016/0045-7825(86)90059-9

Symmetric quadrature rules for simplexes based on sphere close packed lattice arrangements
journal, August 2014

Williams, D. M.; Shunn, L.; Jameson, A.
Journal of Computational and Applied Mathematics, Vol. 266
DOI: 10.1016/j.cam.2014.01.007

Gaussian quadrature formulas for triangles
journal, January 1973

Cowper, G. R.
International Journal for Numerical Methods in Engineering, Vol. 7, Issue 3
DOI: 10.1002/nme.1620070316

New computationally efficient quadrature formulas for pyramidal elements
journal, March 2013

Kubatko, Ethan J.; Yeager, Benjamin A.; Maggi, Ashley L.
Finite Elements in Analysis and Design, Vol. 65
DOI: 10.1016/j.finel.2012.10.012

Computation of moderate-degree fully-symmetric cubature rules on the triangle using symmetric polynomials and algebraic solving
journal, April 2015

Papanicolopulos, Stefanos-Aldo
Computers & Mathematics with Applications, Vol. 69, Issue 7
DOI: 10.1016/j.camwa.2015.02.014

New fully symmetric and rotationally symmetric cubature rules on the triangle using minimal orthonormal bases
journal, March 2016

Papanicolopulos, Stefanos-Aldo
Journal of Computational and Applied Mathematics, Vol. 294
DOI: 10.1016/j.cam.2015.08.001

A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions
journal, January 2010

Xiao, Hong; Gimbutas, Zydrunas
Computers & Mathematics with Applications, Vol. 59, Issue 2
DOI: 10.1016/j.camwa.2009.10.027

Rotation invariant cubature formulas over the n-dimensional unit cube
journal, July 2001

Cools, Ronald; Kim, K. J.
Journal of Computational and Applied Mathematics, Vol. 132, Issue 1
DOI: 10.1016/S0377-0427(00)00595-1

Monomial cubature rules since “Stroud”: a compilation
journal, November 1993

Cools, Ronald; Rabinowitz, Philip
Journal of Computational and Applied Mathematics, Vol. 48, Issue 3
DOI: 10.1016/0377-0427(93)90027-9

Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes
journal, January 2017

Chan, Jesse; Hewett, Russell J.; Warburton, T.
SIAM Journal on Scientific Computing, Vol. 39, Issue 6
DOI: 10.1137/16M1089198

A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables
journal, November 1996

Coleman, Thomas F.; Li, Yuying
SIAM Journal on Optimization, Vol. 6, Issue 4
DOI: 10.1137/S1052623494240456

On the construction of general cubature formula by flat extensions
journal, August 2016

Abril Bucero, Marta; Bajaj, Chandrajit; Mourrain, Bernard
Linear Algebra and its Applications, Vol. 502
DOI: 10.1016/j.laa.2015.09.052

Monomial cubature rules since “Stroud”: a compilation — part 2
journal, November 1999

Cools, Ronald
Journal of Computational and Applied Mathematics, Vol. 112, Issue 1-2
DOI: 10.1016/S0377-0427(99)00229-0

Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra
journal, October 2015

Chin, Eric B.; Lasserre, Jean B.; Sukumar, N.
Computational Mechanics, Vol. 56, Issue 6
DOI: 10.1007/s00466-015-1213-7

Symmetric quadrature rules on a triangle
journal, June 2003

Wandzurat, S.; Xiao, H.
Computers & Mathematics with Applications, Vol. 45, Issue 12
DOI: 10.1016/S0898-1221(03)90004-6

High degree efficient symmetrical Gaussian quadrature rules for the triangle
journal, June 1985

Dunavant, D. A.
International Journal for Numerical Methods in Engineering, Vol. 21, Issue 6
DOI: 10.1002/nme.1620210612

Symmetric gaussian quadrature formulae for tetrahedronal regions
journal, May 1984

Yu, Jinyun
Computer Methods in Applied Mechanics and Engineering, Vol. 43, Issue 3
DOI: 10.1016/0045-7825(84)90072-0

A compendium of FEM integration formulas for symbolic work
journal, December 2004

Felippa, Carlos A.
Engineering Computations, Vol. 21, Issue 8
DOI: 10.1108/02644400410554362

Generalized Gaussian quadrature rules on arbitrary polygons
journal, January 2009

Mousavi, S. E.; Xiao, H.; Sukumar, N.
International Journal for Numerical Methods in Engineering
DOI: 10.1002/nme.2759

Numerical integration on a triangle
journal, January 1977

Hillion, Pierre
International Journal for Numerical Methods in Engineering, Vol. 11, Issue 5
DOI: 10.1002/nme.1620110504

Decoupling simulation accuracy from mesh quality
journal, December 2018

Schneider, Teseo; Hu, Yixin; Dumas, Jérémie
ACM Transactions on Graphics, Vol. 37, Issue 6
DOI: 10.1145/3272127.3275067

Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement
journal, November 2012

Shunn, Lee; Ham, Frank
Journal of Computational and Applied Mathematics, Vol. 236, Issue 17
DOI: 10.1016/j.cam.2012.03.032

Symmetric Gauss Legendre quadrature formulas for composite numerical integration over a triangular surface
journal, May 2007

Rathod, H. T.; Nagaraja, K. V.; Venkatesudu, B.
Applied Mathematics and Computation, Vol. 188, Issue 1
DOI: 10.1016/j.amc.2006.10.041

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Title: High‐order cubature rules for tetrahedra

Citation Formats

Numerical integration on a tetrahedron journal, June 1981

Symmetric Quadrature Formulae for Simplexes journal, January 1970

New computationally efficient quadrature formulas for triangular prism elements journal, March 2013

Invariant Integration Formulas for the n -Simplex by Combinatorial Methods journal, April 1978

Moderate Degree Symmetric Quadrature Rules for the Triangle journal, January 1975

On the identification of symmetric quadrature rules for finite element methods journal, May 2015

p-FEMs in biomechanics: Bones and arteries journal, December 2012

Some criteria for numerically integrated matrices and quadrature formulas for triangles journal, January 1978

Moderate-degree tetrahedral quadrature formulas journal, May 1986

Symmetric quadrature rules for simplexes based on sphere close packed lattice arrangements journal, August 2014

Gaussian quadrature formulas for triangles journal, January 1973

New computationally efficient quadrature formulas for pyramidal elements journal, March 2013

Computation of moderate-degree fully-symmetric cubature rules on the triangle using symmetric polynomials and algebraic solving journal, April 2015

New fully symmetric and rotationally symmetric cubature rules on the triangle using minimal orthonormal bases journal, March 2016

A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions journal, January 2010

Rotation invariant cubature formulas over the n-dimensional unit cube journal, July 2001

Monomial cubature rules since “Stroud”: a compilation journal, November 1993

Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes journal, January 2017

A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables journal, November 1996

On the construction of general cubature formula by flat extensions journal, August 2016

Monomial cubature rules since “Stroud”: a compilation — part 2 journal, November 1999

Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra journal, October 2015

Symmetric quadrature rules on a triangle journal, June 2003

High degree efficient symmetrical Gaussian quadrature rules for the triangle journal, June 1985

Symmetric gaussian quadrature formulae for tetrahedronal regions journal, May 1984

A compendium of FEM integration formulas for symbolic work journal, December 2004

Generalized Gaussian quadrature rules on arbitrary polygons journal, January 2009

Numerical integration on a triangle journal, January 1977

Decoupling simulation accuracy from mesh quality journal, December 2018

Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement journal, November 2012

Symmetric Gauss Legendre quadrature formulas for composite numerical integration over a triangular surface journal, May 2007

Numerical integration on a tetrahedron
journal, June 1981

Symmetric Quadrature Formulae for Simplexes
journal, January 1970

New computationally efficient quadrature formulas for triangular prism elements
journal, March 2013

Invariant Integration Formulas for the n -Simplex by Combinatorial Methods
journal, April 1978

Moderate Degree Symmetric Quadrature Rules for the Triangle
journal, January 1975

On the identification of symmetric quadrature rules for finite element methods
journal, May 2015

p-FEMs in biomechanics: Bones and arteries
journal, December 2012

Some criteria for numerically integrated matrices and quadrature formulas for triangles
journal, January 1978

Moderate-degree tetrahedral quadrature formulas
journal, May 1986

Symmetric quadrature rules for simplexes based on sphere close packed lattice arrangements
journal, August 2014

Gaussian quadrature formulas for triangles
journal, January 1973

New computationally efficient quadrature formulas for pyramidal elements
journal, March 2013

Computation of moderate-degree fully-symmetric cubature rules on the triangle using symmetric polynomials and algebraic solving
journal, April 2015

New fully symmetric and rotationally symmetric cubature rules on the triangle using minimal orthonormal bases
journal, March 2016

A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions
journal, January 2010

Rotation invariant cubature formulas over the n-dimensional unit cube
journal, July 2001

Monomial cubature rules since “Stroud”: a compilation
journal, November 1993

Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes
journal, January 2017

A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables
journal, November 1996

On the construction of general cubature formula by flat extensions
journal, August 2016

Monomial cubature rules since “Stroud”: a compilation — part 2
journal, November 1999

Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra
journal, October 2015

Symmetric quadrature rules on a triangle
journal, June 2003

High degree efficient symmetrical Gaussian quadrature rules for the triangle
journal, June 1985

Symmetric gaussian quadrature formulae for tetrahedronal regions
journal, May 1984

A compendium of FEM integration formulas for symbolic work
journal, December 2004

Generalized Gaussian quadrature rules on arbitrary polygons
journal, January 2009

Numerical integration on a triangle
journal, January 1977

Decoupling simulation accuracy from mesh quality
journal, December 2018

Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement
journal, November 2012

Symmetric Gauss Legendre quadrature formulas for composite numerical integration over a triangular surface
journal, May 2007