Details
| Original language | English |
|---|---|
| Title of host publication | 16th th World Congress in Computational Mechanics (WCCM) |
| Editors | A. Korobenko, M. Laforet, S. Proudhomme, R. Vaziri |
| Publication status | Published - 21 Jul 2024 |
| Event | 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics, WCCM-PANACM 2024 - Vancouver, Canada Duration: 21 Jul 2024 → 26 Jul 2024 |
Abstract
Virtual element methods define their shape functions implicitly (tailored to each element’s geometry), foregoing the typical reference element and transformation scheme usually employed by the finite element method. The formulation leverages the use of polynomial projections supplied by heuristic stabilizations when necessary. These projections are represented by projector matrices, which require the solution of a local system. Elasticity formulations usually employ an L2-projection from a displacement multifield onto a strain multifield, requiring the solution of a considerably larger system than a typical Poisson problem would require, with dense matrices and lots of zeroes. This work presents a way to obtain the projections for elasticity formulation by assembling from the L2-projection for each derivative of the one-field a Poisson formulation, resulting in smaller local systems being solved and more efficient storage. This approach is based on the linearity of both projections and derivatives, and is shown in the examples to preserve the convergence rate of the method.
Keywords
- Elasticity Problems, Poisson Problem, VEM
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
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16th th World Congress in Computational Mechanics (WCCM). ed. / A. Korobenko; M. Laforet; S. Proudhomme; R. Vaziri. 2024.
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
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TY - GEN
T1 - Projector assembly
T2 - 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics, WCCM-PANACM 2024
AU - Moherdaui, Tiago F.
AU - Neto, Alfredo G.
AU - Wriggers, Peter
N1 - Publisher Copyright: © 2024, Scipedia S.L. All rights reserved.
PY - 2024/7/21
Y1 - 2024/7/21
N2 - Virtual element methods define their shape functions implicitly (tailored to each element’s geometry), foregoing the typical reference element and transformation scheme usually employed by the finite element method. The formulation leverages the use of polynomial projections supplied by heuristic stabilizations when necessary. These projections are represented by projector matrices, which require the solution of a local system. Elasticity formulations usually employ an L2-projection from a displacement multifield onto a strain multifield, requiring the solution of a considerably larger system than a typical Poisson problem would require, with dense matrices and lots of zeroes. This work presents a way to obtain the projections for elasticity formulation by assembling from the L2-projection for each derivative of the one-field a Poisson formulation, resulting in smaller local systems being solved and more efficient storage. This approach is based on the linearity of both projections and derivatives, and is shown in the examples to preserve the convergence rate of the method.
AB - Virtual element methods define their shape functions implicitly (tailored to each element’s geometry), foregoing the typical reference element and transformation scheme usually employed by the finite element method. The formulation leverages the use of polynomial projections supplied by heuristic stabilizations when necessary. These projections are represented by projector matrices, which require the solution of a local system. Elasticity formulations usually employ an L2-projection from a displacement multifield onto a strain multifield, requiring the solution of a considerably larger system than a typical Poisson problem would require, with dense matrices and lots of zeroes. This work presents a way to obtain the projections for elasticity formulation by assembling from the L2-projection for each derivative of the one-field a Poisson formulation, resulting in smaller local systems being solved and more efficient storage. This approach is based on the linearity of both projections and derivatives, and is shown in the examples to preserve the convergence rate of the method.
KW - Elasticity Problems
KW - Poisson Problem
KW - VEM
UR - http://www.scopus.com/inward/record.url?scp=85216758326&partnerID=8YFLogxK
U2 - 10.23967/wccm.2024.023
DO - 10.23967/wccm.2024.023
M3 - Conference contribution
AN - SCOPUS:85216758326
BT - 16th th World Congress in Computational Mechanics (WCCM)
A2 - Korobenko, A.
A2 - Laforet, M.
A2 - Proudhomme, S.
A2 - Vaziri, R.
Y2 - 21 July 2024 through 26 July 2024
ER -