arXiv subjects

Pierre Gosselet

Publications and source records attributed to Pierre Gosselet.

At least 19 recordsLinked to original sources

arXiv2025

Multi-scale friction coefficient: From roughness to system computation using deep learning

The presence of surface defects (roughness, surface imperfections, profiles, etc.) in a contact inevitably leads to the modification of its local properties, such as the coefficient of friction. In railway wheelsets, this surface condition is crucial as it dictates appropriate fatigue design for the final use. However, these local phenomena are not well understood and require a real step back. Therefore, the aim of this paper is to propose a multiscale numerical strategy to better understand these phenomena. The multiscale strategy is divided into two steps. Initially, an analysis by the Discrete Element Method (DEM) modelling the interaction of generated rough surfaces is carried out to determine the coefficient of friction. In a second step, the results of DEM are introduced into a structural calculation where the enrichment of the coefficient of friction is done on each finite element contact. Given the wide variety of potential surface defects (size, distribution, height, etc.), a large number of DEM simulations is performed. A specially developed deep learning program is then used to account for these dispersions. The application targeted in this paper is the fitting of a wheel on a railway axle.

physics.class-ph↗

arXiv2024

Conjugate gradient for ill-posed problems: regularization by preconditioning, preconditioning by regularization

This paper investigates using the conjugate gradient iterative solver for ill-posed problems. We show that preconditioner and Tikhonov-regularization work in conjunction. In particular when they employ the same symmetric positive semi-definite operator, a powerful Ritz analysis allows one to estimate at negligible computational cost the solution for any Tikhonov's weight. This enhanced linear solver is applied to the boundary data completion problem and as the inner solver for the optical flow estimator.

math.NA↗

arXiv2024

On the implementation in Abaqus of the global--local iterative coupling and acceleration techniques

This paper presents results and convergence study of the Global--Local Iterative Coupling through the implementation in the commercial software Abaqus making use of the co-simulation engine. A hierarchical modeling and simulation approach is often required to alleviate modeling burdens. Particular focus has been devoted here on convergence acceleration and performance optimization. Two applications in statics with nonlinear material behavior and geometrically nonlinear formulation are considered here: first a holed curved plate under traction with elastic--plastic material, then a pre-stressed bolted joint connecting two plates between each other and subjected to traction load. Three different convergence acceleration techniques are compared in terms of convergence performance and accuracy. An inexact solver strategy is proposed to improve computing time performance. The results show promising results for the coupling technology and constitute a step forward in the availability of non-intrusive multi-scale modeling capabilities for complex structures and assemblies.

math.NA↗

arXiv2024

An Efficient PGD Solver for Structural Dynamics Applications

We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based on the Hamiltonian formalism. The novelty of this work lies in the implementation of a solver that is halfway between Modal Decomposition and the conventional PGD framework, so as to accelerate the fixed-point iteration algorithm. Additional procedures such that Aitken's delta-squared process and mode-orthogonalization are incorporated to ensure convergence and stability of the algorithm. Numerical results regarding the ROM accuracy, time complexity, and scalability are provided to demonstrate the performance of the new solver when applied to dynamic simulation of a three-dimensional structure.

cs.CE↗

arXiv2023

Enhancing the Global/Local Coupling Method: An Asynchronous Parallel Framework

A novel approach is being developed to introduce a parallel asynchronous implementation of non-intrusive global-local coupling. This study examines scenarios involving numerous patches, including those covering the entire structure. By leveraging asynchronous, the method aims to minimize reliance on communication, handle failures effectively, and address load imbalances. Detailed insights into the methodology are presented, accompanied by a demonstration of its performance through an academic case study.

cs.DC↗

arXiv2022

Asynchronous global-local non-invasive coupling for linear elliptic problems

This paper presents the first asynchronous version of the Global/Local non-invasive coupling, capable of dealing efficiently with multiple, possibly adjacent, patches. We give a new interpretation of the coupling in terms of primal domain decomposition method, and we prove the convergence of the relaxed asynchronous iteration. The asynchronous paradigm lifts many bottlenecks of the Global/Local coupling performance. We illustrate the method on several linear elliptic problems as encountered in thermal and elasticity studies.

cs.DC↗

arXiv2022

Asynchronous scalable version of the Global-Local non-invasive coupling

The Global-Local non-invasive coupling is an improvement of the submodeling technique, which permits to locally enhance structure computations by introducing patches with refined models and to take into accounts all the interactions. In order to circumvent its inherently limited computational performance, we propose and implement an asynchronous version of the method. The asynchronous coupling reduces the dependency on communications, failures, and load imbalance. We present the theory and the implementation of the method in the linear case and illustrate its performance on academic cases inspired by actual industrial problems.

cs.DC↗

arXiv2022

Couplage Global-Local en asynchrone pour des problèmes linéaires

An asynchronous parallel version of the non-intrusive global-local coupling is implemented. The case of many patches, including those covering the entire structure, is studied. The asynchronism limits the dependency on communications, failures, and load imbalance. We detail the method and illustrate its performance in an academic case.

cs.DC↗

arXiv2022

Parallel Multiphysics Simulation for the Stabilized Optimal Transportation Meshfree (OTM)

This paper presents a parallel \PG{implementation} for the Optimal Transportation Meshfree (OTM) method on large CPU clusters. Communications are handled with the Message Passing Interface (MPI). The Recursive Coordinate Bisection (RCB) algorithm is utilized for domain decomposition and for implementing dynamic load-balancing strategy. This work involves three new concepts to reduce the computational efforts: Dynamic halo regions, Efficient data management strategies for ease of addition and deletion of nodes and material points using advanced STL container, and nearest neighborhood communication for detection of neighbors and communication. Also, Linked Cell approach has been implemented to further reduce the computational efforts. Parallel performance analysis is investigated for challenging multiphysics applications like Taylor rod impact and serrated chip formation process. Adequate scalability of parallel implementation for these applications is reported.

cs.CE↗

arXiv2021

Constructing the Hamiltonian from the behaviour of a dynamical system by proper symplectic decomposition

The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the Hamiltonian is not the sum of the potential and kinetic energies. On this ground, we want to address the following problem: data being given in the form of one or more structural evolutions, we want to construct an approximation of the Hamiltonian from a covariant snapshot matrix and to perform a symplectic decomposition. We prove the convergence properties of the method when the time discretization is refined. If the data cloud is not enough rich, we extract the principal component of the Hamiltonian corresponding to the leading modes, allowing to perform a model order reduction for very high dimension models. The method is illustrated by a numerical example.

physics.class-ph↗

arXiv2019

Space/time global/local noninvasive coupling strategy: Application to viscoplastic structures

The purpose of this paper is to extend the non-invasive global/local iterative coupling technique [15] to the case of large structures undergoing nonlinear time-dependent evolutions at all scales. It appears that, due to the use of legacy codes, the use of different time grids at the global and local levels is mandatory in order to reach a satisfying level of precision. In this paper two strategies are proposed and compared for elastoviscoplastic models. The questions of the precision and performance of those schemes with respect to a monolithic approach is addressed. The methods are first exposed on a 2D example and then applied on a 3D part of industrial complexity.

cs.CE↗

arXiv2016

Improved recovery of admissible stress in domain decomposition methods - application to heterogeneous structures and new error bounds for FETI-DP

This paper investigates the question of the building of admissible stress field in a substructured context. More precisely we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), (3) a procedure to build admissible fields for FETI-DP and BDDC methods leading to an error bound which separates the contributions of the solver and of the discretization.

math.NA↗

arXiv2016

On the computation of plate assemblies using realistic 3D joint model: a non-intrusive approach

Most large engineering structures are described as assemblies of plates and shells and they are computed as such using adhoc Finite Element packages. In fact their computation in 3D would be much too costly. In this framework, the connections between the parts are often modeled by means of simplified tying models. In order to improve the reliability of such simulations, we propose to apply a non-intrusive technique so as to virtually substitute the simplified connectors by a precise 3D nonlinear model, without modifying the global plate model. Moreover each computation can be conducted on independent optimized software. After a description of the method, examples are used to analyze its performance, and to draw some conclusions on the validity and limitation of both the modeling of junction by rigid connectors and the use of submodeling techniques for the estimation of the carrying capacity of bolted plates.

math.NA↗

arXiv2016

Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a DD iterative solver) from the discretization error (due to the FE), which enables the steering of the iterative solver by the discretization error. These lower bounds are also used to improve the goal-oriented error estimation in a substructured context. Assessments on 2D static linear mechanic problems illustrate the relevance of the separation of sources of error and the lower bounds' independence from the substructuring. We also steer the iterative solver by an objective of precision on a quantity of interest. This strategy consists in a sequence of solvings and takes advantage of adaptive remeshing and recycling of search directions.

math.NA↗

arXiv2016

Substructured formulations of nonlinear structure problems - influence of the interface condition

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a framework where we can swap Newton and DD, so that we solve independent nonlinear problems for each substructure and linear condensed interface problems. The objective is to decrease the number of communications between subdomains and to improve parallelism. Depending on the interface condition, we derive several formulations which are not equivalent, contrarily to the linear case. Primal, dual and mixed variants are described and assessed on a simple plasticity problem.

math.NA↗

arXiv2016

A quasi-optimal coarse problem and an augmented Krylov solver for the Variational Theory of Complex Rays

The Variational Theory of Complex Rays (VTCR) is an indirect Trefftz method designed to study systems governed by Helmholtz-like equations. It uses wave functions to represent the solution inside elements, which reduces the dispersion error compared to classical polynomial approaches but the resulting system is prone to be ill conditioned. This paper gives a simple and original presentation of the VTCR using the discontinuous Galerkin framework and it traces back the ill-conditioning to the accumulation of eigenvalues near zero for the formulation written in terms of wave amplitude. The core of this paper presents an efficient solving strategy that overcomes this issue. The key element is the construction of a search subspace where the condition number is controlled at the cost of a limited decrease of attainable precision. An augmented LSQR solver is then proposed to solve efficiently and accurately the complete system. The approach is successfully applied to different examples.

physics.class-ph↗

arXiv2015

Strict bounding of quantities of interest in computations based on domain decomposition

This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution of reference and adjoint problems : on the one hand the discretization error due to the finite element method and on the other hand the algebraic error due to the use of the iterative solver. Beside practical considerations on the parallel computation of the bounds, it is shown that the interface conformity can be slightly relaxed so that local enrichment or refinement are possible in the subdomains bearing singularities or quantities of interest which simplifies the improvement of the estimation. Academic assessments are given on 2D static linear mechanic problems.

physics.comp-ph↗

arXiv2015

Nonintrusive coupling of 3D and 2D laminated composite models based on finite element 3D recovery

In order to simulate the mechanical behavior of large structures assembled from thin composite panels, we propose a coupling technique which substitutes local 3D models for the global plate model in the critical zones where plate modeling is inadequate. The transition from 3D to 2D is based on stress and displacement distributions associated with Saint-Venant problems which are precalculated automatically for a simple 3D cell. The hybrid plate/3D model is obtained after convergence of a series of iterations between a global plate model of the structure and localized 3D models of the critical zones. This technique is nonintrusive because the global calculations can be carried out using commercial software. Evaluation tests show that convergence is fast and that the resulting hybrid model is very close to a full 3D model.

math.NA↗