A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries

Yi Zhang; Varun Jain; Artur Palha da Silva Clérigo; Marc Gerritsma

A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries

Yi Zhang, Varun Jain, Artur Palha da Silva Clérigo, Marc Gerritsma

Aerodynamics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

In this paper, we present a hybrid mimetic method which solves the mixed formulation of the Poisson problem on curvilinear quadrilateral meshes. The method is hybrid in the sense that the domain is decomposed into multiple disjoint elements and the interelement continuity is enforced using a Lagrange multiplier. The method is mimetic in the sense that the discrete divergence operator is exact. By using the mimetic basis functions and their dual representations, various metric-free discrete terms are obtained. The discrete system can be efficiently solved by first solving a reduced system for the Lagrange multiplier. Numerical experiments which validate the method are presented.

Original language	English
Title of host publication	Proceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publication	Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
Editors	Roger Owen, Rene de Borst, Jason Reese, Chris Pearce
Publisher	International Centre for Numerical Methods in Engineering, CIMNE
Pages	426-437
Number of pages	12
ISBN (Electronic)	9788494731167
Publication status	Published - 2020
Event	6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 - Glasgow, United Kingdom Duration: 11 Jun 2018 → 15 Jun 2018 Conference number: 6

Publication series

Name	Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018

Conference

Conference	6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
Abbreviated title	ECFD 2018
Country/Territory	United Kingdom
City	Glasgow
Period	11/06/18 → 15/06/18

Keywords

Algebraic Dual Polynomials
Broken Spaces
Hybridization
Mimetic Spectral Element Method
Mixed Poisson Formulation

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A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometriesAccepted author manuscript, 674 KB

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Zhang, Y., Jain, V., Palha da Silva Clérigo, A., & Gerritsma, M. (2020). A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries. In R. Owen, R. de Borst, J. Reese, & C. Pearce (Eds.), Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 (pp. 426-437). (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018). International Centre for Numerical Methods in Engineering, CIMNE.

Zhang, Yi ; Jain, Varun ; Palha da Silva Clérigo, Artur et al. / A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries. Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. editor / Roger Owen ; Rene de Borst ; Jason Reese ; Chris Pearce. International Centre for Numerical Methods in Engineering, CIMNE, 2020. pp. 426-437 (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018).

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title = "A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries",

abstract = "In this paper, we present a hybrid mimetic method which solves the mixed formulation of the Poisson problem on curvilinear quadrilateral meshes. The method is hybrid in the sense that the domain is decomposed into multiple disjoint elements and the interelement continuity is enforced using a Lagrange multiplier. The method is mimetic in the sense that the discrete divergence operator is exact. By using the mimetic basis functions and their dual representations, various metric-free discrete terms are obtained. The discrete system can be efficiently solved by first solving a reduced system for the Lagrange multiplier. Numerical experiments which validate the method are presented.",

keywords = "Algebraic Dual Polynomials, Broken Spaces, Hybridization, Mimetic Spectral Element Method, Mixed Poisson Formulation",

author = "Yi Zhang and Varun Jain and {Palha da Silva Cl{\'e}rigo}, Artur and Marc Gerritsma",

year = "2020",

language = "English",

series = "Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018",

publisher = "International Centre for Numerical Methods in Engineering, CIMNE",

pages = "426--437",

editor = "Roger Owen and {de Borst}, Rene and Jason Reese and Chris Pearce",

booktitle = "Proceedings of the 6th European Conference on Computational Mechanics",

note = "6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018, ECFD 2018 ; Conference date: 11-06-2018 Through 15-06-2018",

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Zhang, Y , Jain, V , Palha da Silva Clérigo, A & Gerritsma, M 2020, A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries. in R Owen, R de Borst, J Reese & C Pearce (eds), Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018, International Centre for Numerical Methods in Engineering, CIMNE, pp. 426-437, 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018, Glasgow, United Kingdom, 11/06/18.

A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries. / Zhang, Yi ; Jain, Varun ; Palha da Silva Clérigo, Artur et al.
Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. ed. / Roger Owen; Rene de Borst; Jason Reese; Chris Pearce. International Centre for Numerical Methods in Engineering, CIMNE, 2020. p. 426-437 (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries

AU - Zhang, Yi

AU - Jain, Varun

AU - Palha da Silva Clérigo, Artur

AU - Gerritsma, Marc

N1 - Conference code: 6

PY - 2020

Y1 - 2020

N2 - In this paper, we present a hybrid mimetic method which solves the mixed formulation of the Poisson problem on curvilinear quadrilateral meshes. The method is hybrid in the sense that the domain is decomposed into multiple disjoint elements and the interelement continuity is enforced using a Lagrange multiplier. The method is mimetic in the sense that the discrete divergence operator is exact. By using the mimetic basis functions and their dual representations, various metric-free discrete terms are obtained. The discrete system can be efficiently solved by first solving a reduced system for the Lagrange multiplier. Numerical experiments which validate the method are presented.

AB - In this paper, we present a hybrid mimetic method which solves the mixed formulation of the Poisson problem on curvilinear quadrilateral meshes. The method is hybrid in the sense that the domain is decomposed into multiple disjoint elements and the interelement continuity is enforced using a Lagrange multiplier. The method is mimetic in the sense that the discrete divergence operator is exact. By using the mimetic basis functions and their dual representations, various metric-free discrete terms are obtained. The discrete system can be efficiently solved by first solving a reduced system for the Lagrange multiplier. Numerical experiments which validate the method are presented.

KW - Algebraic Dual Polynomials

KW - Broken Spaces

KW - Hybridization

KW - Mimetic Spectral Element Method

KW - Mixed Poisson Formulation

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T3 - Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018

SP - 426

EP - 437

BT - Proceedings of the 6th European Conference on Computational Mechanics

A2 - Owen, Roger

A2 - de Borst, Rene

A2 - Reese, Jason

A2 - Pearce, Chris

PB - International Centre for Numerical Methods in Engineering, CIMNE

T2 - 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018

Y2 - 11 June 2018 through 15 June 2018

ER -

Zhang Y , Jain V , Palha da Silva Clérigo A , Gerritsma M. A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries. In Owen R, de Borst R, Reese J, Pearce C, editors, Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. International Centre for Numerical Methods in Engineering, CIMNE. 2020. p. 426-437. (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018).

A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries

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Mimetic Spectral Element Method and Extensions toward Higher Computational Efficiency

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