arXiv subjects

Frederic Magoules

Publications and source records attributed to Frederic Magoules.

At least 19 recordsLinked to original sources

arXiv2024

Frequency range non-Lipschitz parametric optimization of a noise absorption

In the framework of the optimal wave energy absorption, we solve theoretically and numerically a parametric shape optimization problem to find the optimal distribution of absorbing material in the reflexive one defined by a characteristic function in the Robin-type boundary condition associated with the Helmholtz equation. Robin boundary condition can be given on a part or the all boundary of a bounded ($\epsilon$, $\infty$)-domain of R n . The geometry of the partially absorbing boundary is fixed, but allowed to be non-Lipschitz, for example, fractal. It is defined as the support of a d-upper regular measure with d $\in$]n -2, n[. Using the well-posedness properties of the model, for any fixed volume fraction of the absorbing material, we establish the existence of at least one optimal distribution minimizing the acoustical energy on a fixed frequency range of the relaxation problem. Thanks to the shape derivative of the energy functional, also existing for non-Lipschitz boundaries, we implement (in the two-dimensional case) the gradient descent method and find the optimal distribution with 50% of the absorbent material on a frequency range with better performances than the 100% absorbent boundary. The same type of performance is also obtained by the genetic method.

math.AP↗

arXiv2023

A Hybrid GNN approach for predicting node data for 3D meshes

Metal forging is used to manufacture dies. We require the best set of input parameters for the process to be efficient. Currently, we predict the best parameters using the finite element method by generating simulations for the different initial conditions, which is a time-consuming process. In this paper, introduce a hybrid approach that helps in processing and generating new data simulations using a surrogate graph neural network model based on graph convolutions, having a cheaper time cost. We also introduce a hybrid approach that helps in processing and generating new data simulations using the model. Given a dataset representing meshes, our focus is on the conversion of the available information into a graph or point cloud structure. This new representation enables deep learning. The predicted result is similar, with a low error when compared to that produced using the finite element method. The new models have outperformed existing PointNet and simple graph neural network models when applied to produce the simulations.

cs.LG↗

arXiv2022

Point-Cloud-based Deep Learning Models for Finite Element Analysis

In this paper, we explore point-cloud based deep learning models to analyze numerical simulations arising from finite element analysis. The objective is to classify automatically the results of the simulations without tedious human intervention. Two models are here presented: the Point-Net classification model and the Dynamic Graph Convolutional Neural Net model. Both trained point-cloud deep learning models performed well on experiments with finite element analysis arising from automotive industry. The proposed models show promise in automatizing the analysis process of finite element simulations. An accuracy of 79.17% and 94.5% is obtained for the Point-Net and the Dynamic Graph Convolutional Neural Net model respectively.

math.NA↗

arXiv2022

Graph Neural Network-based Surrogate Models for Finite Element Analysis

Current simulation of metal forging processes use advanced finite element methods. Such methods consist of solving mathematical equations, which takes a significant amount of time for the simulation to complete. Computational time can be prohibitive for parametric response surface exploration tasks. In this paper, we propose as an alternative, a Graph Neural Network-based graph prediction model to act as a surrogate model for parameters search space exploration and which exhibits a time cost reduced by an order of magnitude. Numerical experiments show that this new model outperforms the Point-Net model and the Dynamic Graph Convolutional Neural Net model.

math.NA↗

arXiv2022

Multilayer Perceptron-based Surrogate Models for Finite Element Analysis

Many Partial Differential Equations (PDEs) do not have analytical solution, and can only be solved by numerical methods. In this context, Physics-Informed Neural Networks (PINN) have become important in the last decades, since it uses a neural network and physical conditions to approximate any functions. This paper focuses on hypertuning of a PINN, used to solve a PDE. The behavior of the approximated solution when we change the learning rate or the activation function (sigmoid, hyperbolic tangent, GELU, ReLU and ELU) is here analyzed. A comparative study is done to determine the best characteristics in the problem, as well as to find a learning rate that allows fast and satisfactory learning. GELU and hyperbolic tangent activation functions exhibit better performance than other activation functions. A suitable choice of the learning rate results in higher accuracy and faster convergence.

math.NA↗

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

JACK2: a new high-level communication library for parallel iterative methods

In this paper, we address the problem of designing a distributed application meant to run both classical and asynchronous iterations. MPI libraries are very popular and widely used in the scientific community, however asynchronous iterative methods raise non-negligible difficulties about the efficient management of communication requests and buffers. Moreover, a convergence detection issue is introduced, which requires the implementation of one of the various state-of-the-art termination methods, which are not necessarily highly reliable for most computational environments. We propose here an MPI-based communication library which handles all these issues in a non-intrusive manner, providing a unique interface for implementing both classical and asynchronous iterations. Few details are highlighted about our approach to achieve best communication rates and ensure accurate convergence detection. Experimental results on two supercomputers confirmed the low overhead communication costs introduced, and the effectiveness of our library.

cs.DC↗

arXiv2022

Distributed asynchronous convergence detection without detection protocol

In this paper, we address the problem of detecting the moment when an ongoing asynchronous parallel iterative process can be terminated to provide a sufficiently precise solution to a fixed-point problem being solved. Formulating the detection problem as a global solution identification problem, we analyze the snapshot-based approach, which is the only one that allows for exact global residual error computation. From a recently developed approximate snapshot protocol providing a reliable global residual error, we experimentally investigate here, as well, the reliability of a global residual error computed without any prior particular detection mechanism. Results on a single-site supercomputer successfully show that such high-performance computing platforms possibly provide computational environments stable enough to allow for simply resorting to non-blocking reduction operations for computing reliable global residual errors, which provides noticeable time saving, at both implementation and execution levels.

cs.DC↗

arXiv2021

Iterative Krylov Methods for Acoustic Problems on Graphics Processing Unit

This paper deals with linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetic using double precision. An analysis of their uses within iterative Krylov methods is presented to solve acoustic problems. Numerical experiments performed on a set of acoustic matrices arising from the modelisation of acoustic phenomena inside a car compartment are collected, and outline the performance, robustness and effectiveness of our algorithms, with a speed-up up to 28x for dot product, 9.8x for sparse matrix-vector product and solvers.

math.NA↗

arXiv2021

Fast and Green Computing with Graphics Processing Units for solving Sparse Linear Systems

In this paper, we aim to introduce a new perspective when comparing highly parallelized algorithms on GPU: the energy consumption of the GPU. We give an analysis of the performance of linear algebra operations, including addition of vectors, element-wise product, dot product and sparse matrix-vector product, in order to validate our experimental protocol. We also analyze their uses within conjugate gradient method for solving the gravity equations on Graphics Processing Unit (GPU). Cusp library is considered and compared to our own implementation with a set of real matrices arrising from the Chicxulub crater and obtained by the finite element discretization of the gravity equations. The experiments demonstrate the performance and robustness of our implementation in terms of energy efficiency.

math.NA↗

arXiv2021

Accelerated solution of Helmholtz equation with Iterative Krylov Methods on GPU

This paper gives an analysis and an evaluation of linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetics with double precision. Knowing the performance of these operations, iterative Krylov methods are considered to solve the acoustic problem efficiently. Numerical experiments carried out on a set of acoustic matrices arising from the modelisation of acoustic phenomena within a cylinder and a car compartment are exposed, exhibiting the performance, robustness and efficiency of our algorithms, with a ratio up to 27x for dot product, 10x for sparse matrix-vector product and solvers in complex double precision arithmetics.

math.NA↗

arXiv2021

Stochastic Optimized Schwarz Methods for the Gravity Equations on Graphics Processing Unit

Low order, sequential or non-massively parallel finite elements are generaly used for three-dimensional gravity modelling. In this paper, in order to obtain better gravity anomaly solutions in heterogeneous media, we solve the gravimetry problem using massively parallel high order finite elements on hybrid multi-CPU/GPU clusters. Parallel algorithms well suited for such hybrid architectures have to be designed. A new stochastic-based optimization procedure for the optimized Schwarz method is here presented, implemented and tuned to graphical cards processors units. Numerical experiments performed on a reallistic test case, demonstrates the robustness and efficiency of the proposed method and of its implementation on massive multi-CPU/GPU architectures.

math.NA↗

arXiv2021

On the stability and performance of the solution of sparse linear systems by partitioned procedures

In this paper, we present, evaluate and analyse the performance of parallel synchronous Jacobi algorithms by different partitioned procedures including band-row splitting, band-row sparsity pattern splitting and substructuring splitting, when solving sparse large linear systems. Numerical experiments performed on a set of academic 3D Laplace equation and on a real gravity matrices arising from the Chicxulub crater are exhibited, and show the impact of splitting on parallel synchronous iterations when solving sparse large linear systems. The numerical results clearly show the interest of substructuring methods compared to band-row splitting strategies.

math.NA↗

arXiv2021

Coupling and Simulation of Fluid-Structure Interaction Problems for Automotive Sun-roof on Graphics Processing Unit

In this paper, the authors propose an analysis of the frequency response function in a car compartment, subject to some fluctuating pressure distribution along the open cavity of the sun-roof at the top of a car. Coupling of a computational fluid dynamics and of a computational acoustics code is considered to simulate the acoustic fluid-structure interaction problem. Iterative Krylov methods and domain decomposition methods, tuned on Graphic Processing Unit (GPU), are considered to solve the acoustic problem with complex number arithmetics with double precision. Numerical simulations illustrate the efficiency, robustness and accuracy of the proposed approaches.

math.NA↗

arXiv2021

Asynchronous parareal time discretization for partial differential equations

Asynchronous iterations are more and more investigated for both scaling and fault-resilience purpose on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks, this paper advocates a novel application direction targeting time-decomposed time-parallel approaches. Specifically, an asynchronous iterative model is derived from the Parareal scheme, for which convergence and speedup analysis are then conducted. It turned out that Parareal and async-Parareal feature very close convergence conditions, asymptotically equivalent, including the finite-time termination property. Based on a computational cost model aware of unsteady communication delays, our speedup analysis shows the potential performance gain from asynchronous iterations, which is confirmed by some experimental case of heat evolution on a homogeneous supercomputer. This primary work clearly suggests possible further benefits from asynchronous iterations.

cs.DC↗

arXiv2019

Using asynchronous simulation approach for interactive simulation

This paper discusses about the advantage of using asynchronous simulation in the case of interactive simulation in which user can steer and control parameters during a simulation in progress. synchronous models allow to compute each iteration faster to address the issues of performance needed in an highly interactive context, and our hypothesis is that get partial results faster is better than getting synchronized and final results to take a decision, in a interactive simulation context.

cs.DC↗

arXiv2019

Interactive 3D fluid simulation: steering the simulation in progress using Lattice Boltzmann Method

This paper describes a work in progress about software and hardware architecture to steer and control an ongoing fluid simulation in a context of a serious game application. We propose to use the Lattice Boltzmann Method as the simulation approach considering that it can provide fully parallel algorithms to reach interactive time and because it is easier to change parameters while the simulation is in progress remaining physically relevant than more classical simulation approaches. We describe which parameters we can modify and how we solve technical issues of interactive steering and we finally show an application of our interactive fluid simulation approach of water dam phenomena.

cs.GR↗