Parallel Adaptive Multigrid Methods for 3D Finite Element Structural Problems

Adaptive mesh refinement can be used to greatly reduce the number of finite elements required to solve a structural problem to a desired accuracy. Multigrid methods can greatly accelerate the solution of a system of equations. Parallel computing can be used to further reduce computational times. Efficent parallelization of adaptive multigrid methods requires the load to be balanced on all meshes during all steps of the solution. Additionally, efficent parallel performance must be obtained on the coarse meshes of the multigrid hierarchy to produce an overall efficent algorithm. When parallel computing, adaptive refinement, and multigrid are combined solution times can be reduced by orders of magnitude as compared to more conventional methods.