Extending the p-Version of Finite Elements by an Octree-Based Hierarchy

In structural mechanics, a large variety of finite element approaches are used, some of them – especially of p-type – without an inherent hierarchical substructuring. This often turns out to be a drawback. By embedding the finite element decomposition into an octree structure, the elements can be arranged in a hierarchical way, which does not only open the door to efficient iterative solvers based on the classical nested dissection algorithm, but also allows to speed up the solution process in case only parts of the underlying geometric model are changed, as only those parts and their region of direct influence have to be recomputed.     «

In structural mechanics, a large variety of finite element approaches are used, some of them – especially of p-type – without an inherent hierarchical substructuring. This often turns out to be a drawback. By embedding the finite element decomposition into an octree structure, the elements can be arranged in a hierarchical way, which does not only open the door to efficient iterative solvers based on the classical nested dissection algorithm, but also allows to speed up the solution process in c...     »