Maîtrise foncière, pratiques agricoles durables et protection de la ressource en eau : quels outils d’intervention sur les AAC ?

Enjeu de santé publique et de préservation des milieux, la protection des captages et de la ressource en eau fait l’objet d’une série de dispositifs mis en oeuvre à la fois de façon règlementaire et volontaire. Les acteurs de la protection, à l’échelon local, ont notamment recours à toute la gamme d’outils fonciers : de la maîtrise de l’usage du sol à l’acquisition foncière en propriété. En plus, la mise en oeuvre de pratiques agricoles durables, par le biais du bail environnemental notamment, est une orientation forte pour concilier activité agricole et protection des ressources en eau. Les expériences observables en Île-de-France font état des obstacles rencontrés pour la mise en oeuvre de ce type d’actions. La principale difficulté, en dehors de la capacité des gestionnaires, concerne le rapport entre la profession agricole et l’instrument foncier. En Île-de-France, la situation est exacerbée compte tenu du contexte de pression foncière forte

Learnable Earth Parser: Discovering 3D Prototypes in Aerial Scans

We propose an unsupervised method for parsing large 3D scans of real-world scenes into interpretable parts. Our goal is to provide a practical tool for analyzing 3D scenes with unique characteristics in the context of aerial surveying and mapping, without relying on application-specific user annotations. Our approach is based on a probabilistic reconstruction model that decomposes an input 3D point cloud into a small set of learned prototypical shapes. Our model provides an interpretable reconstruction of complex scenes and leads to relevant instance and semantic segmentations. To demonstrate the usefulness of our results, we introduce a novel dataset of seven diverse aerial LiDAR scans. We show that our method outperforms state-of-the-art unsupervised methods in terms of decomposition accuracy while remaining visually interpretable. Our method offers significant advantage over existing approaches, as it does not require any manual annotations, making it a practical and efficient tool for 3D scene analysis. Our code and dataset are available at https://imagine.enpc.fr/~loiseaur/learnable-earth-parse

Generation of viscous grids at ridges and corners

An extension of Löhner (AIAA‐93‐3348‐CP , 1993) for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for Reynolds‐averaged Navier–Stokes computations. Multiple point normals are introduced along ridges and corners. The original technique generates a semi‐structured boundary layer of prismatic elements growing along point normals. Therefore, extra degenerated faces must be introduced to take into account the multiple growth curves at ridges and corners and produce a valid topological surface triangulation. The major task of the algorithm consists in recovering conformity in the surface mesh triangulation, which has been lost due to the introduction of the virtual faces. The procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges. Each case is highlighted in detail. Special boundary conditions such as symmetry planes and periodic boundary conditions are also handled. Several complex geometries have been chosen to illustrate the proposed procedure, and timings are given, showing that the new module does not place any extra burden on the previous semi‐structured approach

On the ‘most normal’ normal

Given a set of normals in ℛ3, two algorithms are presented to compute the ‘most normal’ normal. The ‘most normal’ normal is the normal that minimizes the maximal angle with the given set of normals. A direct application is provided supposing a surface triangulation is available. The set of normals may represent either the face normals of the faces surrounding a point or the point normals of the points surrounding a point. The first algorithm is iterative and straightforward, and is inspired by the one proposed by Pirzadeh (AIAA Paper 94‐0417 , 1994). The second gives more insight into the complete problem as it provides the unique solution explicitly. It would correspond to the general extension of the algorithm presented by Kallinderis (AIAA‐92‐2721 , 1992)

The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid–object interactions

The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics including thermal convection–diffusion, Comput Struct 2004;83:1459–75; Idelsohn S, Oñate E, Del Pin F, A Lagrangian meshless finite element method applied to fluid–structure interaction problems, Comput Struct 2003;81:655–71; Idelsohn SR, Oñate E, Del Pin F, The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Num Methods Eng 2004;61:964–84] where critical parts of the continuum are discretized into particles. The nodes treated as particles transport their momentum and physical properties in a Lagrangian way while the rest of the nodes may move in an Arbitrary Lagrangian–Eulerian (ALE) frame. In order to solve the governing equations that represent the continuum, the particles are connected by means of a Delaunay Triangulation [Idelsohn SR, Oñate E, Calvo N, Del Pin F, The meshless finite element method, Int J Num Methods Eng 2003;58(4)]. The resulting partition is a mesh where the Finite Element Method is applied to solve the equations of motion. The application of a fully Lagrangian formulation on the particles provides a natural and simple way to track free surfaces as well as to compute contacts in an accurate and robust fashion. Furthermore, the usage of an ALE formulation allows large mesh deformation with larger time steps than the full Lagrangian scheme

Incompressible Lagrangian fluid flow with thermal coupling

In this monograph is presented a method for the solution of an incompressible viscous fluid flow with heat transfer and solidification usin a fully Lagrangian description on the motion. The originality of this method consists in assembling various concepts and techniques which appear naturally due to the Lagrangian formulation.Postprint (published version

Iterative solution applied to the Helmholtz equation: Complex deflation on unstructured grids

Extensions of deflation techniques developed for the Poisson and Navier equations (Aubry et al., 2008; Mut et al., 2010; Löhner et al., 2011; Aubry et al., 2011) [1], [2], [3], [4] are presented for the Helmholtz equation. Numerous difficulties arise compared to the previous case. After discretization, the matrix is now indefinite without Sommerfeld boundary conditions, or complex with them. It is generally symmetric complex but not Hermitian, discarding optimal short recurrences from an iterative solver viewpoint (Saad, 2003) [5]. Furthermore, the kernel of the operator in an infinite space typically does not belong to the discrete space. The choice of the deflation space is discussed, as well as the relationship between dispersion error and solver convergence. Similarly to the symmetric definite positive (SPD) case, subdomain deflation accelerates convergence if the low frequency eigenmodes are well described. However, the analytic eigenvectors are well represented only if the dispersion error is low. CPU savings are therefore restricted to a low to mid frequency regime compared to the mesh size, which could be still relevant from an application viewpoint, given the ease of implementation

Deflated preconditioned conjugate gradient solvers for linear elasticity

Extensions of deflation techniques previously developed for the Poisson equation to static elasticity are presented. Compared to the (scalar) Poisson equation (J. Comput. Phys. 2008; 227 (24):10196–10208; Int. J. Numer. Meth. Engng 2010; DOI: 10.1002/nme.2932; Int. J. Numer. Meth. Biomed. Engng 2010; 26 (1):73–85), the elasticity equations represent a system of equations, giving rise to more complex low‐frequency modes (Multigrid . Elsevier: Amsterdam, 2000). In particular, the straightforward extension from the scalar case does not provide generally satisfactory convergence. However, a simple modification allows to recover the remarkable acceleration in convergence and CPU time reached in the scalar case. Numerous examples and timings are provided in a serial and a parallel context and show the dramatic improvements of up to two orders of magnitude in CPU time for grids with moderate graph depths compared to the non‐deflated version. Furthermore, a monotonic decrease of iterations with increasing subdomains, as well as a remarkable acceleration for very few subdomains are also observed if all the rigid body modes are included

Deflated preconditioned conjugate gradient solvers for the Pressure–Poisson equation

A deflated preconditioned conjugate gradient technique has been developed for the solution of the Pressure–Poisson equation within an incompressible flow solver. The deflation is done using a region-based decomposition of the unknowns, making it extremely simple to implement. The procedure has shown a considerable reduction in the number of iterations. For grids with large graph-depth the savings exceed an order of magnitude. Furthermore, the technique has shown a remarkable insensitivity to the number of groups/regions chosen, and to the way the groups are formed

Fast numerical solutions of patient‐specific blood flows in 3D arterial systems

The study of hemodynamics in arterial models constructed from patient‐specific medical images requires the solution of the incompressible flow equations in geometries characterized by complex branching tubular structures. The main challenge with this kind of geometries is that the convergence rate of the pressure Poisson solver is dominated by the graph depth of the computational grid. This paper presents a deflated preconditioned conjugate gradients (DPCG) algorithm for accelerating the pressure Poisson solver. A subspace deflation technique is used to approximate the lowest eigenvalues along the tubular domains. This methodology was tested with an idealized cylindrical model and three patient‐specific models of cerebral arteries and aneurysms constructed from medical images. For these cases, the number of iterations decreased by up to a factor of 16, while the total CPU time was reduced by up to 4 times when compared with the standard PCG solver