Objectives

The work package aims at providing octree and anisotropic meshing capabilities, on the base of existing libraries available to the project partners. Work will be done to provide both the capability of robustly performing an initial mesh of the volume, and to provide a mesh refinement/coarsening engine based on mesh modification.

Initial meshing will be done by constructing an octree mesh around an embedded approximation of the object of interest. This step will include both the construction of hexa-only mesh with hanging nodes, and the generation of conforming discretization by fitting tetrahedral patterns to the octree discretization.

The mesh adaptation engine will be constructed on the basis of the MMG software, combining local mesh adaptation with an aggressive rebalancing strategy. Such step will include the possibility of performing anisotropic adaptation according to the user-provided metric tensor.

In the case of octree meshes, current WP will also provide foundational work towards allowing 4D adaptivity for the space-time solvers.

Task 2.1: Development and deployment of a MPI parallel octree management library

This task will focus on the development of a parallel octree, capable of representing objects up to a prescribed level of accuracy. Implementation will be based on either the p4est GPL library or on homegrown libraries based on the capabilities current available to the partners. The new library will target high parallel efficiency.

Task 2.2: Development of a MPI-parallel anisotropic adaptive Mesh generation library

The task will focus on the adaptation of an existing conforming mesh so to achieve compliance to a target metric tensor. The work will be done on the base of the existing serial MMG meshing library, which will be used for MPI -local adaptation. MPI will be tackled according to the preexistent experience of the Task leader, by combining the local
refinement with global goal-oriented mesh rebalancing steps.

Task 2.3: Development of adjoint-based error estimation routines

The task will provide error estimation capabilities which will be exposed to the MLMC engine. The task goal is to enable providing goal-oriented adaptivity, so to be able to reduce the error in the given target quantity to a user-prescribed threshold. Discrete adjoint-based approaches will be used to provide the required capabilities. Such solvers will also
be designed to effectively participate of the developments in WP3 on parallel-in-time solvers as well as on space-time parallelization.

Task 2.4: Interfacing of CFD solvers to the newly developed capabilities

This work, to be performed in close collaboration between INRIA and CIMNE, will focus on adapting the CFD solvers so to take full advantage of the novel mesh adaptation capabilities. This will rely on the adjoint-based error estimates to be developed in T2.3 and will expose the new capabilities to the MLMC engine.