Pierre Gosselet

Univ. Lille, CNRS, Centrale Lille · LaMcube - Laboratoire de Mécanique, Multiphysique, Multiéchelle - UMR 9013

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 ve...

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.

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 in...

This paper presents a parallel 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 involve...

We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, dedicated to nonlinear substructured and condensed fo...

This work studies the convergence properties of the mixed non-overlapping domain decomposition method (DDM) commonly named “Latin method”. As all DDM, the Latin method is sensitive to near-interface heterogeneity and irregularity. Using a simple yet fresh point of view, we analyze the role of the Robin parameters as well as of the second level (coa...

This paper presents a new parallel mesh generation method leading to subdomains of shape well-suited to Schur based domain decomposition methods such as the FETI and BDD solvers. Starting from a coarse mesh, subdomains meshes are created in parallel through hierarchical mesh refinement and morphing techniques. The proposed methodology aims at limit...

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 follo...

This paper proposes and studies three methods for the identification of cracks in linear elastic bodies. They are based on the reciprocity gap principle which they extend to the case of partially redundant boundary data. The methods are all assessed on an academic 2D case, then the most appealing is more deeply analysed and illustrated on a 3D test...

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 follo...

This article introduces two strategies to reduce the memory cost of the Adaptive Multipreconditioned FETI method (AMPFETI) while preserving its capability to solve ill conditioned systems efficiently. Their common principle is to gather search directions into aggregates which are frequently adapted in order to achieve the best compromise between th...

When carrying out non-destructive testing of mechanical parts, the identification of boundary conditionsfrom measurements on other boundaries is problematic. This problem is known as data completionproblem, or Cauchy problem, which is present in a wide range of applications.However, the Cauchy problem for elliptic PDEs is known to be mathematically...

We study the Cauchy problem in the framework of static linear elasticity and its resolution via the Steklov-Poincaré approach. In the linear Gaussian framework, the straightforward application of Bayes theory leads to formulas allowing to deduce the uncertainty on the identified field from the noise level. We use a truncated Ritz decomposition of t...

The aim of this paper is to provide, for a reader not familiar with the non-intrusive coupling method, the simplest possible example on which all the different iterative coupling strategies can be solved by hands. Among them, the basic algorithm, Aitken’s method, mixed interface conditions...A drawback of this example is that, for some acceleration...

We study the Cauchy problem in the framework of static linear elasticity and its resolution via the Steklov-Poincaré approach. In the linear Gaussian framework, the straightforward application of Bayes theory leads to formulas allowing to deduce the uncertainty on the identified field from the noise level. We use a truncated Ritz decomposition of t...

We study the reciprocity gap method [5] for the identification of planar cracks in the framework of three dimensionallinear elasticity. In order to achieve better accuracy on thick domains, we propose to use polynomial test functions instead of Fourier series. We also propose to improve the solution by various regularization techniques that are tes...

On s’intéresse dans cette contribution à l’identification de fissures internes dans des pièces mécaniques à partir de mesures des déformations de celles-ci sous des sollicitations quasi-statiques. On utilise pour ce faire la méthode de l’écart à la réciprocité. Une procédure sera proposée afin de se passer de la nécessité, très contraignante pour c...

This paper proposes to confront a mixed domain decomposition method with industrial computations, in par- ticular the simulation of quasi-static assemblies with frictional contact between the parts. The method is imple- mented in a non-invasive manner around an industrial finite element software. The performance of the algorithm is studied on indus...

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 satisfyi...

The non-invasive global–local coupling algorithm is revisited and shown to realize a simple implementation of the optimized non-overlapping Schwarz domain decomposition method. This connection is used to propose and compare several acceleration techniques, and to extend the approach to non conforming meshes.

In this article, a method to accelerate the solution of multiple right‐hand side problems when using the adaptive multi‐preconditioned finite element tearing and interconnecting algorithm is presented. This is done by deflating the conjugate gradient algorithm by means of a coarse space, which is built by a simplification of the recently published...

We propose a study of primal and dual Steklov-Poincaré approaches for the data completion problem in linear elasticity. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Different preconditioning and acceleration strategies are evaluated. We show that costless filtering of th...

In the framework of non-destructive control of mechanical parts, the question of the identification of macroscopical cracks from indirect measurements is relevant. In this contribution, we will focus on the crack identification from the measurement of the displacement of the boundary of a part submitted to a known mechanical loading. Mathematically...

This article presents a study of primal and dual Steklov‐Poincare˜ approaches for the identification of unknown boundary conditions of elliptic problems. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Different preconditioning and acceleration strategies are evaluated. We...

This article presents a new method to recycle the solution space of an adaptive multi‐preconditioned finite element tearing and interconnecting (AMP‐FETI) algorithm in the case where the same operator is solved for multiple right‐hand sides like in linear structural dynamics. It accelerates the computation from the second time step on by applying a...

In the framework of the non-destructive control of mechanical components, the question of the identification of internal macroscopical cracks from indirect measurements is relevant. In this contribution, we focus on the identification of cracks from the measurement of the displacement at the boundary of a domain submitted to a known mechanical load...

A multiscale extension for a parallel non‐invasive mixed domain decomposition method is presented. After briefly exposing our non‐invasive implementation of the Latin method, we present how the scalability of the algorithm is obtained by the partial verification of the constitutive law of the interfaces. We propose a new interpretation of the class...

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which c...

Abstract The purpose of this article is to assess the adaptive multipreconditioned FETI solvers (AMPFETI) on real industrial problems and hardware. The multipreconditioned FETI algorithm (first introduced as Simultaneous FETI (Gosselet et al., 2015) is a non-overlapping domain decomposition method which exhibits good robustness properties without r...

We apply a multipreconditioned domain decomposition method based on Finite Element Tearing and Interconnecting to linear structural dynamics with highly heterogeneous material properties. A recently published method to build and select the multiple directions is presented and applied. We hint at possible problems when localized phenomena are consid...

A non-invasive implementation of the Latin domain decomposition method for frictional contact problems is described. The formulation implies to deal with mixed (Robin) conditions on the faces of the subdomains, which is not a classical feature of commercial software. Therefore we propose a new implementation of the linear stage of the Latin method...

On propose l'étude d'un préconditionneur dual pour la résolution par la méthode de Steklov-Poincaré et l'algorithme du gradient conjugué du problème de Cauchy connu pour être mal posé au sens de la stabilité. L'utilisation de ce préconditionneur revient à utiliser la méthode de KMF accélérée par un solveur de Krylov. On montre qu'il est possible de...

This article presents a study of primal and dual Steklov-Poincaré approaches for the identi cation of unknown boundary conditions of elliptic problems. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Di�erent preconditioning and acceler-ation strategies are evaluated. We sh...

Numerical evidence is provided that there are non-constant permittivity profiles which force solutions to a two-dimensional coupled moving boundary problem modelling microelectromechanical systems to be positive, while the corresponding small-aspect ratio model produces solutions which are always non-positive.

This paper is devoted to the study of a micro-macro LaTIn-based Domain Decomposition Method for which the partitioning, the geometry and the boundary conditions play a major role in the number of iterations to convergence and in the scalability. To confront these obstacles, an analysis of the macroscopic space and of the search direction–two parame...

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 reliabilit...

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...

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element and domain decomposition methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a domain decomposition iterative solver) from the discretization error (due to the...

Preconditioned Krylov subspace methods are powerful tools for solving linear systems but sometimes they converge very slowly, and often after a long stagnation. A natural way to fix this is by enlarging the space in which the solution is computed at each iteration. Following this idea, we propose in this note two multipreconditioned algorithms: mul...

Domain Decomposition methods often exhibit very poor performance when applied to engineering problems with large heterogeneities. In particular for heterogeneities along domain interfaces the iterative techniques to solve the interface problem are lacking an efficient preconditioner. Recently a robust approach, named FETI-Geneo, was proposed where...

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...

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 pap...

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 li...

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...

This paper deals with the estimation of the distance between the solution of a static linear mechanic problem and its approximation by the finite element method solved with a non-overlapping domain decomposition method (FETI or BDD). We propose a new strict upper bound of the error which separates the contribution of the iterative solver and the co...

Résumé — This paper proposes a novel technique to reduce the computational burden associated with the simulation of structural failure by concentrating the computational effort where it is most needed, i.e. in the localisation zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe...

This paper focuses on the construction of statically admissible stress fields (SA-fields) for a posteriori error estimation. In the context of verification, the recovery of such fields enables to provide strict upper bounds of the energy norm of the discretization error between the known finite element solution and the unavailable exact solution. T...

This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition Methods are mainly used as a solver for the tangent problem to be solved at each iteration of a Newton-Raphson al...

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature, we present a procedure based on a selection of relevant approximations of the eigenspaces for extracting, selec...

This paper presents a strategy for a posteriori error estimation for substructured problems solved by non-overlapping domain decomposition methods. We focus on global estimates of the discretization error obtained through the error in constitutive relation for linear mechanical problems. Our method allows to compute error estimate in a fully parall...

This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated surfaces. In order to achieve an accurate prediction of the quasi-static response, a very refined discretizat...

We study the implementation of a domain decomposition method for structures with quasi-incompressible components. We chose a mixed formulation where the pressure field is discontinuous on the interfaces between substructures. We propose an extension of classical preconditioners to this class of problems. The numerical simulation of the mechanical b...

A monolithic strategy based on an hybrid domain decomposition method for the numerical simulation of multiphysic problems is presented. It relies on a "physical" choice of primal interface unknowns. First numerical assessments are described for poroelasticity problems.

This paper presents a three-scale computational strategy for the study of composite modeled at the mesoscale so that delamination can be reliably simulated. The solver is based on a LaTIn approach so that nonlinearities can be tackled at the local scale. We show how search directions which are parameters of the method need to be updated according t...

This paper presents a two-scale approximation of the Schur complement of a subdomain's stiffness matrix, obtained by combining local (i.e. element strips) and global (i.e. homogenized) contributions. This approximation is used in the context of a coupling strategy that is designed to embed local plasticity and geometric details into a small region...

We present numerical enhancements of a multiscale domain decomposition strategy based on a LaTIn solver and dedicated to the computation of the debounding in laminated composites. We show that the classical scale separation is irrelevant in the process zones, which results in a drop in the convergence rate of the strategy. We show that performing n...