Mesh adaptation with large deformations : theory, algorithms and implementation

(eng) Today, one of the major limitations of the finite element method remains its high computational cost. For that reason, mesh adaptivity has an important role to play since it provides a strong control of the distribution of the computational resources in time and space. Recently, mesh adaptivity has also become an interesting tool for the problems involving large displacements or deformations: industrial processes, fluid-structure interaction problems, crash simulations, biomedical applications, ... The classical node repositioning techniques do not always succeed in returning an acceptable mesh, and the solution that consists in re-meshing the domain suffers from important drawbacks (hardly parallelizable, global projections of the solution). This PhD dissertation focuses on the development of a mesh adaptation method able to handle arbitrarily large deformations of the computational domain. For that purpose, an approach combining a global node repositioning technique with local mesh modifications is chosen. The mesh adaptation methods based on local mesh modifications are first investigated in the framework of the two-phase flow problems. A method allowing large domain deformations is then proposed and evaluated. The approach is extended to meet some common requirements of the finite element analyses like the compatibility of the mesh to a CAD model and the handling of boundary layer meshes. The developments presented in this dissertation have been implemented in the open source library MAdLib, which is intended to fill a gap in the set of available open source softwares by providing efficient mesh adaptation capabilities for tetrahedral meshes.