TY - EJOU
AU - Mehraban, Arash
AU - Tufo, Henry
AU - Sture, Stein
AU - Regueiro, Richard
TI - Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes
T2 - Computer Modeling in Engineering \& Sciences
PY - 2021
VL - 129
IS - 3
SN - 1526-1506
AB - 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.
KW - Matrix-free; higher-order; finite element; parallel; linear elasticity; multigrid solvers; unstructured meshes
DO - 10.32604/cmes.2021.017476