An automatic mesh coarsening technique for three dimensional anisotropic meshes

This work is devoted to the design of a mesh generation technique able to produce a sequence of 3-D coarsened unstructured meshes from an initial anisotropic one. The coarsening algorithm uses an initial mesh and a metric field obtained from an analysis of the natural metric of this initial mesh. First, an initial natural metric (i.e a metric into which each simplicial element of the mesh is equilateral) is produced from the initial anisotropic mesh. Then the eigenvalues of this metric are modified and used together with the initial mesh to produce a coarsened mesh. In this way, the directions of anisotropies of the initial mesh are respected while the mesh spacing can be increased. This procedure can be repeated in order to produce a sequence of semi-coarsened meshes suitable for multigrid acceleration. The efficiency of this procedure is shown on examples of anisotropic meshes involving element aspect ratio as high as $10^{5}$

An automatic mesh coarsening technique for three dimensional anisotropic meshes

This work is devoted to the design of a mesh generation technique able to produce a sequence of 3-D coarsened unstructured meshes from an initial anisotropic one. The coarsening algorithm uses an initial mesh and a metric field obtained from an analysis of the natural metric of this initial mesh. First, an initial natural metric (i.e a metric into which each simplicial element of the mesh is equilateral) is produced from the initial anisotropic mesh. Then the eigenvalues of this metric are modified and used together with the initial mesh to produce a coarsened mesh. In this way, the directions of anisotropies of the initial mesh are respected while the mesh spacing can be increased. This procedure can be repeated in order to produce a sequence of semi-coarsened meshes suitable for multigrid acceleration. The efficiency of this procedure is shown on examples of anisotropic meshes involving element aspect ratio as high as $10^{5}$

Automatic coarsening of three dimensional anisotropic unstructured meshes for multigrid applications

International audienceThis paper describes an algorithm designed for the automatic coarsening of three-dimensional unstructured simplicial meshes. This algorithm can handle very anisotropic meshes like the ones typically used to capture the boundary layers in CFD with Low Reynolds turbulence modeling that can have aspect ratio as high as 104. It is based on the concept of mesh generation governed by metrics and on the use of a natural metric mapping the initial (fine) mesh into an equilateral one. The paper discusses and compares several ways to define node based metric from element based metric. Then the semi-coarsening algorithm is described. Several application examples are presented, including a full three-dimensional complex model of an aircraft with extremely high anisotropy

Energy Concerns with HPC Systems and Applications

For various reasons including those related to climate changes, {\em energy} has become a critical concern in all relevant activities and technical designs. For the specific case of computer activities, the problem is exacerbated with the emergence and pervasiveness of the so called {\em intelligent devices}. From the application side, we point out the special topic of {\em Artificial Intelligence}, who clearly needs an efficient computing support in order to succeed in its purpose of being a {\em ubiquitous assistant}. There are mainly two contexts where {\em energy} is one of the top priority concerns: {\em embedded computing} and {\em supercomputing}. For the former, power consumption is critical because the amount of energy that is available for the devices is limited. For the latter, the heat dissipated is a serious source of failure and the financial cost related to energy is likely to be a significant part of the maintenance budget. On a single computer, the problem is commonly considered through the electrical power consumption. This paper, written in the form of a survey, we depict the landscape of energy concerns in computer activities, both from the hardware and the software standpoints.Comment: 20 page

Identification of vortex in unstructured mesh with graph neural networks

Deep learning has been employed to identify flow characteristics from Computational Fluid Dynamics (CFD) databases to assist the researcher to better understand the flow field, to optimize the geometry design and to select the correct CFD configuration for corresponding flow characteristics. Convolutional Neural Network (CNN) is one of the most popular algorithms used to extract and identify flow features. However its use, without any additional flow field interpolation, is limited to the simple domain geometry and regular meshes which limits its application to real industrial cases where complex geometry and irregular meshes are usually used. Aiming at the aforementioned problems, we present a Graph Neural Network (GNN) based model with U-Net architecture to identify the vortex in CFD results on unstructured meshes. The graph generation and graph hierarchy construction using algebraic multigrid method from CFD meshes are introduced. A vortex auto-labeling method is proposed to label vortex regions in 2D CFD meshes. We precise our approach by firstly optimizing the input set on CNNs, then benchmarking current GNN kernels against CNN model and evaluating the performances of GNN kernels in terms of classification accuracy, training efficiency and identified vortex morphology. Finally, we demonstrate the adaptability of our approach to unstructured meshes and generality to unseen cases with different turbulence models at different Reynolds numbers.Comment: Accepted by the journal Computers & Fluid

Conformal hexahedral mesh coarsening by agglomeration

International audienceReservoir simulation involves to compute dynamic flow of different phases ina porous medium. The initial state of the reservoir is usually precomputed viageo-statistics methods, extrapolating measures of the terrain. so, the inputof reservoir simulation is given as a fine mesh containing heterogeneous dataIn this paper, we describe an agglomeration strategy, to dynamicallycoarsen this fine hex-dominant mesh. The adaptivitymay be driven by physics and/or geometric estimators. Ideally, the coars-ening should be applied locally in low gradient regions, whereas high gradientregions keep the fine mesh

High-Performance Computing: Dos and Don’ts

Computational fluid dynamics (CFD) is the main field of computational mechanics that has historically benefited from advances in high-performance computing. High-performance computing involves several techniques to make a simulation efficient and fast, such as distributed memory parallelism, shared memory parallelism, vectorization, memory access optimizations, etc. As an introduction, we present the anatomy of supercomputers, with special emphasis on HPC aspects relevant to CFD. Then, we develop some of the HPC concepts and numerical techniques applied to the complete CFD simulation framework: from preprocess (meshing) to postprocess (visualization) through the simulation itself (assembly and iterative solvers)

Predictive load balancing schemes for adaptive finite element solvers

International audienceThis work is motivated by the success of the anisotropic adaptive finite element methods in accurately simulating complex physical systems in science and engineering. The parallel implementation of anisotropic adaptive finite element methods is a challenging task for which load imbalance continue to be a significant bottleneck in the global simulation efficiency. We have developed and optimized in the last years, tools and algorithms to manage efficiently the dynamic load balancing in the framework of parallel anisotropic mesh adaptation [1-4]. However, there still complicated and challenging to predict a quantified estimation of parallel workload of adaptive finite element meshes. Indeed, the mesh adaptation procedure changes dynamically the size of the mesh over all the processes. This mechanism is managed by an anisotropic error estimator that allows to equi-distribute the error over the entire domain by refining and coarsening the mesh in the regions where it is needed [5-7]. In other words, the size of the problem changes permanently along the runtime execution. The leading questions that arise from this analysis are: how to derive a scalability model to measure the parallel efficiency of a dynamic adaptive simulation? And how to estimate quantitatively the workload needed to achieve the remeshing stage? We propose in this paper, an anisotropic a posteriori error estimator that controls the error due to mesh discretization in all space directions. From the a posteriori error analysis, we get an optimal metric (optimal mesh) as a minimum of an error estimator function constrained by a given number of elements. The optimal metric obtained is used to build an optimal mesh for the given number of elements and also to derive a quantitative estimation of the work that will be done in the remeshing stage. We conduct performance analysis over different multi-phase flows [8] to highlight effectiveness of the proposed approach