Parallel implementation of immersed boundary adaptive FEM or how to avoid mesh generation in a mesh-based method

Abstract

Finite element method (FEM) typically relies on computational meshes composed of elements forming a nonoverlapping partition of the computational domain. However, generating these meshes of suficient quality can be challenging and time-consuming, especially for very complex geometries used, e.g. in 3D printing. As a potential remedy, ideas of the immersed boundary method have been incorporated into FEM. We present a parallel implementation of an immersed boundary adaptive FEM. In order to achieve suficient resolution at the boundary, local mesh refinement driven towards boundary is used. For large meshes distributed over a large number of processors, the resulting systems have to be solved by parallel iterative solvers. We present the method and demonstrate its performance for a complex problem of linear elasticity with meshes refined adaptively towards the area with the largest stress for achieving better accuracy within these regions.