A hybrid mimetic spectral element method for three-dimensional linear elasticity problems

Yi Zhang; Joël Fisser; Marc Gerritsma

doi:10.1016/j.jcp.2021.110179

A hybrid mimetic spectral element method for three-dimensional linear elasticity problems

Yi Zhang^*, Joël Fisser, Marc Gerritsma

^*Corresponding author for this work

Aerodynamics

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Abstract

We introduce a domain decomposition structure-preserving method based on a hybrid mimetic spectral element method for three-dimensional linear elasticity problems in curvilinear conforming structured meshes. The method is an equilibrium method which satisfies pointwise equilibrium of forces. The domain decomposition is established through hybridization which first allows for an inter-element normal stress discontinuity and then enforces the normal stress continuity using a Lagrange multiplier which turns out to be the displacement in the trace space. Dual basis functions are employed to simplify the discretization and to obtain a higher sparsity. Numerical tests supporting the method are presented.

Original language	English
Article number	110179
Number of pages	20
Journal	Journal of Computational Physics
Volume	433
DOIs	https://doi.org/10.1016/j.jcp.2021.110179
Publication status	Published - 2021

Keywords

De Rham complex
Domain decomposition
Hybridization
Lagrange multiplier
Mimetic spectral element method
Variational principle

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10.1016/j.jcp.2021.110179

1-s2.0-S0021999121000747-mainFinal published version, 811 KBLicence: CC BY

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abstract = "We introduce a domain decomposition structure-preserving method based on a hybrid mimetic spectral element method for three-dimensional linear elasticity problems in curvilinear conforming structured meshes. The method is an equilibrium method which satisfies pointwise equilibrium of forces. The domain decomposition is established through hybridization which first allows for an inter-element normal stress discontinuity and then enforces the normal stress continuity using a Lagrange multiplier which turns out to be the displacement in the trace space. Dual basis functions are employed to simplify the discretization and to obtain a higher sparsity. Numerical tests supporting the method are presented.",

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language = "English",

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T1 - A hybrid mimetic spectral element method for three-dimensional linear elasticity problems

AU - Zhang, Yi

AU - Fisser, Joël

AU - Gerritsma, Marc

PY - 2021

Y1 - 2021

N2 - We introduce a domain decomposition structure-preserving method based on a hybrid mimetic spectral element method for three-dimensional linear elasticity problems in curvilinear conforming structured meshes. The method is an equilibrium method which satisfies pointwise equilibrium of forces. The domain decomposition is established through hybridization which first allows for an inter-element normal stress discontinuity and then enforces the normal stress continuity using a Lagrange multiplier which turns out to be the displacement in the trace space. Dual basis functions are employed to simplify the discretization and to obtain a higher sparsity. Numerical tests supporting the method are presented.

AB - We introduce a domain decomposition structure-preserving method based on a hybrid mimetic spectral element method for three-dimensional linear elasticity problems in curvilinear conforming structured meshes. The method is an equilibrium method which satisfies pointwise equilibrium of forces. The domain decomposition is established through hybridization which first allows for an inter-element normal stress discontinuity and then enforces the normal stress continuity using a Lagrange multiplier which turns out to be the displacement in the trace space. Dual basis functions are employed to simplify the discretization and to obtain a higher sparsity. Numerical tests supporting the method are presented.

KW - De Rham complex

KW - Domain decomposition

KW - Hybridization

KW - Lagrange multiplier

KW - Mimetic spectral element method

KW - Variational principle

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DO - 10.1016/j.jcp.2021.110179

M3 - Article

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SN - 0021-9991

VL - 433

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 110179

ER -

A hybrid mimetic spectral element method for three-dimensional linear elasticity problems

Abstract

Keywords

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Mimetic Spectral Element Method and Extensions toward Higher Computational Efficiency

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