An object oriented 3-dimensional adaptive Finite Element Program

Rainer Niekamp, Ottmar Klaas, Erwin Stein University Hannover, Germany

Abstract

For the computation of large 3-dimensional Finite Element problems it is advantageous to use

• adaptivity to keep the number of unknowns as small as possible and to control the discretization error

• parallel algorithms to have access to (the potential unlimited) capacities of parallel computers in storage and computational speed

• iterative solvers, since they are efficient parallizable and are able to solve the problem with fewer operations (O(n*log n)) compared to direct solvers (O(n*n))

We present a 3-dimensional adaptive refinement procedure on hexahedral elements producing regular hierarchical meshes without hanging nodes. The algorithms are implemented in the object oriented Finite Element program PARAFEP. The solution of the unstructured system of equations is performed by a preconditioned conjugate gradient solver. The preconditioning is based on multilevel methods.

Examples showing the functionality and effectivity of the implemented algorithms are presented.