Open Access
ARTICLE
Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes
Arash Mehraban1, Henry Tufo1, Stein Sture2, Richard Regueiro2,*
1 Department of Computer Science, University of Colorado Boulder, Boulder, CO, USA
2 Department of Civil, Environmental, and Architectural Engineering, University of Colorado Boulder, Boulder, CO, USA
* Corresponding Author:Richard Regueiro. Email:
(This article belongs to the Special Issue: Advances in Computational Mechanics and Optimization
To celebrate the 95th birthday of Professor Karl Stark Pister)
Computer Modeling in Engineering & Sciences 2021, 129(3), 1283-1303. https://doi.org/10.32604/cmes.2021.017476
Received 13 May 2021; Accepted 02 July 2021; Issue published 25 November 2021
Abstract
Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity, yet are computationally expensive.
To address the computational expense, the paper presents a matrix-free, displacement-based, higher-order, hexahedral finite element implementation of compressible and nearly-compressible (ν → 0.5) linear isotropic elasticity
at small strain with p-multigrid preconditioning. The cost, solve time, and scalability of the implementation with
respect to strain energy error are investigated for polynomial order
p = 1, 2, 3, 4 for compressible elasticity, and
p =
2, 3, 4 for nearly-incompressible elasticity, on different number of CPU cores for a tube bending problem. In the
context of this matrix-free implementation, higher-order polynomials (
p = 3, 4) generally are faster in achieving
better accuracy in the solution than lower-order polynomials (
p = 1, 2). However, for a beam bending simulation
with stress concentration (singularity), it is demonstrated that higher-order finite elements do not improve the
spatial order of convergence, even though accuracy is improved.
Keywords
Cite This Article
APA Style
Mehraban, A., Tufo, H., Sture, S., Regueiro, R. (2021). Matrix-free higher-order finite element method for parallel simulation of compressible and nearly-incompressible linear elasticity on unstructured meshes. Computer Modeling in Engineering & Sciences, 129(3), 1283-1303. https://doi.org/10.32604/cmes.2021.017476
Vancouver Style
Mehraban A, Tufo H, Sture S, Regueiro R. Matrix-free higher-order finite element method for parallel simulation of compressible and nearly-incompressible linear elasticity on unstructured meshes. Comput Model Eng Sci. 2021;129(3):1283-1303 https://doi.org/10.32604/cmes.2021.017476
IEEE Style
A. Mehraban, H. Tufo, S. Sture, and R. Regueiro "Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes," Comput. Model. Eng. Sci., vol. 129, no. 3, pp. 1283-1303. 2021. https://doi.org/10.32604/cmes.2021.017476