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Discrete and algorithmic geometry

Many numerical simulation codes require to discretize the study geometric domain into a finite set of elementary cells, called a mesh, to perform local numerical computations. Our aim is to cover all the aspects of the mesh management for HPC codes. It means to handle the mesh generation process from the CAD geometry definition to the mesh (re)-partitioning during the simulation code execution. Our final goal being to provide software for FMV volume codes, we mainly focus on three research tracks:

  1. Generating hexahedral block-structured meshes by both considering how to prepare the CAD geometry to be split into blocks and how to generate/optimize a block structure for different categories of CAD models
  2. Designing parallel meshing algorithms that cover any type of meshes (triangular/quad, tetrahedral/hexahedral, hybrid) and mixing different levels of parallelism (distributed and shared memory mainly)
  3. Providing partitioning algorithms and tools to (re)partition meshes and numerical simulation data while dealing with multi-physics code requirements (restitution time, multi-objective functions) and hardware constraints (heterogeneous process unit and memory limitations).

Keywords: Hexahedral meshing, B-Rep, Block structure, graph and mesh partitioning, discrete optimization, parallel computing, topology, multi-level techniques, muti-objective problems, computational geometry, linear and non-linear optimization problem, mixed-integer problems, frame fields, polycube.