Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Dedicated to Professor Karl Stark Pister for his 95th birthday Elasticity on Unstructured Meshes  

作　　者：Arash Mehraban Henry Tufo Stein Sture Richard Regueiro 

机构地区：[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

出　　处：《Computer Modeling in Engineering & Sciences》2021年第12期1283-1303,共21页工程与科学中的计算机建模（英文）

基　　金：The research relied on computational resources[29]provided by the University of Colorado Boulder Research Computing Group,which is supported by the National1302 CMES,2021,vol.129,no.3 Science Foundation(Awards ACI-1532235 and ACI-1532236);University of Colorado Boulder,and Colorado State University.

摘　　要：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.

关 键 词：MATRIX-FREE HIGHER-ORDER finite element parallel linear elasticity multigrid solvers unstructured meshes 

分 类 号：O17[理学—数学]