Projector assembly
bridging Poisson and elasticity formulations
- verfasst von
- Tiago F. Moherdaui, Alfredo G. Neto, Peter Wriggers
- 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.
- Organisationseinheit(en)
-
Institut für Kontinuumsmechanik
- Externe Organisation(en)
-
Universidade de Sao Paulo
- Typ
- Aufsatz in Konferenzband
- Publikationsdatum
- 21.07.2024
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Maschinenbau
- Elektronische Version(en)
-
https://doi.org/10.23967/wccm.2024.023 (Zugang:
Offen)
