@Article{cmes.2021.017476,
AUTHOR = {Arash Mehraban, Henry Tufo, Stein Sture, Richard Regueiro},
TITLE = {Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {129},
YEAR = {2021},
NUMBER = {3},
PAGES = {1283--1303},
URL = {http://www.techscience.com/CMES/v129n3/45689},
ISSN = {1526-1506},
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.},
DOI = {10.32604/cmes.2021.017476}
}