Franck LEDOUX
My reserach field consists in defining and developing new methods and tools in the environment of HPC numerical simulation codes. More precisely, I focus my research on the generation and manipulation of meshes for numerical simulation purposes.. It can be divided into three main areas:
- The generation of quadrilateral and hexahedral meshes
- Partitioning of graphs and meshes
- The adaptation of meshes into hybrid concurrent and distributed parallelism.
This activity is carried out in close collaboration with the IBISC laboratory at the University of Evry-Val-d’Essonne (Paris-Saclay), where I have been an associate professor (PAST) in Computer Science since 2009.
Proceedings of the 2024 International Meshing Roundtable (IMR), 2024
abstract
Abstract
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes. Existing techniques for high-order mesh generation typically output meshes with same polynomial order for all elements. However, high order elements away from curvilinear boundaries or interfaces increase the computational cost of the simulation without increasing geometric accuracy. In prior work [5, 21], we have presented one such approach for generating body-fitted uniform-order meshes that takes a given mesh and morphs it to align with the surface of interest prescribed as the zero isocontour of a level-set function. We extend this method to generate mixed-order meshes such that curved surfaces of the domain are discretized with high-order elements, while low-order elements are used elsewhere. Numerical experiments demonstrate the robustness of the approach and show that it can be used to generate mixed-order meshes that are much more efficient than high uniform-order meshes. The proposed approach is purely algebraic, and extends to different types of elements (quadrilaterals/triangles/tetrahedron/hexahedra) in two- and three-dimensions.
Abstract
Quad meshing is a very well-studied domain for many years. Although the problem can generally be considered solved, many approaches do not provide adequate inputs for Computational Fluid Dynamics (CFD) and, in our case, hypersonic flow simulations. Such simulations require very strong monitoring of cell size and direction. To our knowledge, engineers do this manually with the help of interactive software. In this work we propose an automatic algorithm to generate full quadrilateral block structured mesh for the purpose of hypersonic flow simulation. Using this approach we can handle some simulation input like the angle of attack and the boundary layer definition. We will present here 2D results of computation on a hypersonic vehicle using the meshes generated by our method.
International Meshing Roundtable, 2023
abstract
Abstract
Quad meshing is a very well-studied domain for many years. While the problem can be globally considered as solved, many approaches do not provide suitable inputs for Computational Fluid Dynamics (CFD) and in our case for supersonic flow simulations. Such simulations require a very strong control on the cell size and direction. To our knowledge, engineers ensure this control manually using interactive software. In this work we propose an automatic algorithm to generate full quadrilateral block structured mesh for the purpose of supersonic flow simulation. We handle some simulation input like the angle of attack and the boundary layer definition. Our approach generates adequate 2D meshes and is designed to be extensible in 3D.
SIAM International Meshing Roundtable, 2023
abstract
Abstract
Nowadays for real study cases, the generation of full block structured hexahedral meshes is mainly an interactive and very-time consuming process realized by highly-qualified engineers. To this purpose, they use interactive software where they handle and modify complex block structures with operations like block removal, block insertion, O-grid insertion, propagation of block splitting, propagation of meshing parameters along layers of blocks and so on. Such operations are error-prone and modifying or adding an operation is a very tedious work. In this work, we propose to formally define hexahedral block structures and main associated operations in the model of n-dimensional generalized map. This model provides topological invariant and a systematic handling of geometric data that allows us to ensure the expected robustness.
Abstract
Polycube-maps are used as base-complexes in various fields of computational geometry, including the generation of regular all-hexahedral meshes free of internal singularities. However, the strict alignment constraints behind polycube-based methods make their computation challenging for CAD models used in numerical simulation via finite element method (FEM). We propose a novel approach based on an evolutionary algorithm to robustly compute polycube-maps in this context. We address the labelling problem, which aims to precompute polycube alignment by assigning one of the base axes to each boundary face on the input. Previous research has described ways to initialize and improve a labelling via greedy local fixes. However, such algorithms lack robustness and often converge to inaccurate solutions for complex geometries. Our proposed framework alleviates this issue by embedding labelling operations in an evolutionary heuristic, defining fitness, crossover, and mutations in the context of labelling optimization. We evaluate our method on a thousand smooth and CAD meshes, showing Evocube converges to accurate labellings on a wide range of shapes. The limitations of our method are also discussed thoroughly.
Mesh Generation and Adaptation: Cutting-Edge Techniques, Springer International Publishing, p. 69-94, 2022
abstract
Abstract
In this chapter, we deal with the problem of mesh conversion for coupling lagrangian and eulerian simulation codes. More specifically, we focus on hexahedral meshes, which are known as pretty difficult to generate and handle. Starting from an eulerian hexahedral mesh, i.e. a hexahedral mesh where each cell contains several materials, we provide a full-automatic process that generates a lagrangian hexahedral mesh, i.e. a hexahedral mesh where each cell contains a single material. This process is simulation-driven in the meaning that the we guarantee that the generated mesh can be used by a simulation code (minimal quality for individual cells), and we try and preserve the volume and location of each material as best as possible. In other words, the obtained lagrangian mesh fits the input eulerian mesh with high-fidelity. To do it, we interleave several advanced meshing treatments--mesh smoothing, mesh refinement, sheet insertion, discrete material reconstruction, discrepancy computation, in a fully integrated pipeline. Our solution is evaluated on 2D and 3D examples representative of CFD simulation (Computational Fluid Dynamics).
2020 Proceedings of the SIAM Workshop on Combinatorial Scientific Computing, p. 85-95, 2020
Proceedings of the 28th International Meshing Roundtable, 2019
abstract
Abstract
Hexahedral mesh generation using overlay grid methods has the benefit of being fully automatic, requiring minimal user input. These methods follow a mesh-first approach where an initial mesh, usually a grid, is used to overlay the reference geometry. Procedures to modify the initial mesh are then employed to best capture the geometry to get a conformal all-hex mesh [1\]. One of the main drawbacks of those methods is the resulting mesh quality. While the interior of the mesh remains the same as the initial mesh, cells located at the material interfaces can end up quite deformed or even inverted, making the mesh totally useless for most numerical simulation codes. Considering an input mesh carrying volume fractions of the materials, the main purpose of the presented work is to ensure a minimal cell quality. Our method draws upon the overlay grid pipeline described in [2\] where several steps (cell assignment correction, interface reconstruction, mesh adaptation) are altered to control cell quality.
Abstract
In this work, we provide a new post-processing procedure for automatically adjusting node locations of an all-hex mesh to better match the volume of a reference geometry. This process is particularly well-suited for mesh-first approaches, as overlay grid ones. In practice, hexahedral meshes generated via an overlay grid procedure, where a precise reference geometry representation is unknown or is impractical to use, do not provide for precise volumetric preservation. A discrete volume fraction representation of the reference geometry MI on an overlay grid is compared with a volume fraction representation of a 3D finite element mesh MO. This work introduces the notion of localized discrepancy between MI and MO and uses it to design a procedure that relocates mesh nodes to more accurately match a reference geometry. We demonstrate this procedure on a wide range of hexahedral meshes generated with the Sculpt code and show improved volumetric preservation while still maintaining acceptable mesh quality.
Procedia Engineering, p. 258-270, 2017-01
abstract
Abstract
We propose a new post-processing procedure for automatically adjusting node locations of an all-hex mesh to better match the volume of a reference geometry. Hexahedral meshes generated via an overlay grid procedure, where a precise reference geometry representation is unknown or is impractical to use, do not provide for precise volumetric preservation. A discrete volume fraction representation of the reference geometry MI on an overlay grid is compared with a volume fraction representation of a 3D finite element mesh MO. This work proposes a procedure that uses the localized discrepancy between MI and MO to drive node relocation operations to more accurately match a reference geometry. We demonstrate this procedure on a wide range of hexahedral meshes generated with the Sculpt code and show improved volumetric preservation while still maintaining acceptable mesh quality.
Euro-Par 2017: Parallel Processing, Springer International Publishing, p. 594-606, 2017
abstract
Abstract
In this paper, we present a fine-grained multi-stage metric-based triangular remeshing algorithm on manycore and NUMA architectures. It is motivated by the dynamically evolving data dependencies and workload of such irregular algorithms, often resulting in poor performance and data locality at high number of cores. In this context, we devise a multi-stage algorithm in which a task graph is built for each kernel. Parallelism is then extracted through fine-grained independent set, maximal cardinality matching and graph coloring heuristics. In addition to index ranges precalculation, a dual-step atomic-based synchronization scheme is used for nodal data updates. Despite its intractable latency-boundness, a good overall scalability is achieved on a NUMA dual-socket Intel Haswell and a dual-memory Intel KNL computing nodes (64 cores). The relevance of our synchronization scheme is highlighted through a comparison with the state-of-the-art.
Conférence d'informatique en Parallélisme, Architecture et Système (Compas'2016), 2016-07
Euro-Par 2016: Parallel Processing - 22nd International European Conference on Parallel and Distributed Computing, Grenoble, FR, August 24-26, 2016, Proceedings, p. 196-208, 2016
ROADEF - 15ème Congrès Annuel de La Société Française de Recherche Opérationnelle et d'aide à La Décision, Société française de recherche opérationnelle et d'aide à la décision, 2014-02
CSC 14, p. 2, 2014
Proceedings of the 21st International Meshing Roundtable, Springer Berlin Heidelberg, p. 315-332, 2013
abstract
Abstract
Generating a full hexahedral mesh for any 3D geometric domain is still a challenging problem. Among the different attempts, the octree-based methods are the most efficient from an engineering point of view. But the main drawback of such methods is the lack of control near the boundary. In this work, we propose an a posteriori technique based on the notion of the fundamental mesh in order to improve the mesh quality near the boundary. This approach is based on the resolution of a constraint problem defined on the topology of the CAD model that we have to discretize.
Proceedings of the 6th International Conference on Adaptive Modeling and Simulation, ADMOS 2013, p. 412-422, 2013
abstract
Abstract
In numerous computational engineering applications, hexahedral meshes may be preferred over tetrahedral meshes. However, automatic hexahedral meshing remains an unsolved issue and thus generating a hexahedral mesh is known as a time-consuming stage that requires a lot of user interactions in the simulation process. A possible way for designing and optimizing a CAD model or a geometric shape requires parametric studies where the shape is enriched by inserting geometric details into it. Then we must \"adapt\" the initial mesh and not generate it anew for each new detail taken into account. In order to perform such studies with hexahedral meshes, we provide an imprinting method allowing us to automatically add geometric details into an existing mesh. This addition is done using geometric projections, sheets (layers of hexahedral elements) insertions and combinatorial algorithms while preserving the hexahedral mesh structure as best as possible.
J. Comput. Phys., p. 4324-4354, 2012
The Eighth International Conference on Engineering Computational Technology, p. 4, 2012