Article
Mathematics, Applied
Yunan Yang, Alex Townsend, Daniel Appelo
Summary: Anderson acceleration (AA) is utilized in this paper to improve the convergence of fixed-point iterations by modifying the norm to H-s norm. AA based on the H-2 norm is found to be well-suited for solving fixed-point operators derived from second-order elliptic differential operators, including the Helmholtz equation.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
L. B. Mohammed, A. Kilicman, A. U. Saje
Summary: In this paper, new algorithms are proposed to solve the split equality fixed-point problems for total quasi-asymptotically nonexpansive mappings in Hilbert spaces. Convergence criteria for the proposed algorithms are established and numerical results are provided to justify the theoretical results. The results of this paper provide a unified framework for studying problems involving different classes of mappings.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Operations Research & Management Science
Xuezhong Wang, Ping Wei, Yimin Wei
Summary: This paper presents a fixed point iterative approach for solving third-order tensor linear complementarity problems (TLCP). Theoretical analysis shows that TLCP is equivalent to a fixed point equation under tensor T-product. Based on the fixed point equation, a fixed point iterative method is proposed, and its convergence is studied. Estimations of the convergence rate are also provided. The computer-simulation results further validate the effectiveness of the proposed method in solving TLCP.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Shih-Hsiang Chang
Summary: Existence and uniqueness results have been established for a general nonlinear fourth-order two-point boundary value problem with general linear homogeneous boundary conditions. The proofs are based on the Banach fixed-point theorem, and a fixed-point iterative method for finding the solution of the problem is proposed.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Songting Luo, Qing Huo Liu
Summary: In this paper, a simple approach based on fixed point iterations is presented for numerically solving the high frequency vector wave equations, where the problem is transformed into a fixed point problem related to an exponential operator. The associated functional evaluations are achieved by unconditionally stable operator-splitting based pseudospectral schemes, allowing for large step sizes to efficiently reach the approximated fixed point for prescribed termination criteria. For the sub-operator related to non-constant relative permeability, the Krylov subspace method or Taylor expansion is used to approximate its exponential. Furthermore, the Anderson acceleration is incorporated to accelerate the convergence of the fixed-point iterations. Numerical experiments demonstrate the accuracy and efficiency of the method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Artificial Intelligence
Peisong Wang, Xiangyu He, Qiang Chen, Anda Cheng, Qingshan Liu, Jian Cheng
Summary: The proposed FFN framework efficiently converts all weights into ternary values, achieving minimal performance degradation without supervised retraining. It enables significant compression while maintaining comparable accuracy in large-scale ImageNet classification and MS COCO object detection tasks.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Engineering, Multidisciplinary
Luyao Yang, Hao Chen, Haocheng Yu, Jin Qiu, Shuxian Zhu
Summary: A fixed-point iterative method based on intelligent optimization is proposed to optimize the reconstruction of binary images in Discrete Tomography. Experimental data shows that this method is significantly more efficient than the branch and bound method.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Applied
San-hua Wang, Yu-xin Zhang, Wen-jun Huang
Summary: This paper considers algorithms for finding common solutions of strong vector equilibrium and fixed point problems of multivalued mappings. First, a Minty vector equilibrium problem is introduced and the relationship between the Minty vector equilibrium problem and the strong equilibrium problem is discussed. Then, projection iterative methods are proposed by applying the Minty vector equilibrium problem, and some convergence results are established in Hilbert spaces. The main results obtained in this paper develop and improve some recent works in this field.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics
Konrawut Khammahawong, Parin Chaipunya, Kamonrat Sombut
Summary: The aim of this research is to propose a new iterative procedure for approximating common fixed points of nonexpansive mappings in Hadamard manifolds, and discuss the convergence theorem of the proposed method under certain conditions. Numerical examples are provided to support the results for clarity. Furthermore, the suggested approach is applied to solve inclusion problems and convex feasibility problems.
Article
Engineering, Electrical & Electronic
Guang Deng, Fernando Galetto
Summary: In this paper, the use of fixed-point acceleration techniques to address the slow processing speed of iterative reverse filters is proposed. The existing reverse filters are interpreted as fixed-point iterations and their relationship with gradient descent is discussed. Extensive experimental results on the performance of fixed-point acceleration techniques named Anderson, Chebyshev, Irons, and Wynn are presented, and compared with gradient descent acceleration. Key findings include the convergent effect of Anderson acceleration, the efficiency of the T-method with acceleration, and the processing speed improvement for all reverse filters with acceleration techniques.
SIGNAL IMAGE AND VIDEO PROCESSING
(2023)
Article
Mathematics
Yuanheng Wang, Tiantian Xu, Jen-Chih Yao, Bingnan Jiang
Summary: This paper proposes a new method to solve the split feasibility problem and the fixed-point problem involving quasi-nonexpansive mappings. By relaxing the conditions of the operator and considering the inertial iteration and adaptive step size, our algorithm achieves better convergence and faster convergence rate compared to previous algorithms.
Article
Mathematics, Applied
Faeem Ali, Javid Ali, Izhar Uddin
Summary: In this paper, a new fixed point iterative method based on Green's function is introduced and a strong convergence result is proved for the integral operator. Numerical examples are presented to validate the effectiveness, applicability, and high efficiency of the proposed method. The results extend and generalize the corresponding results in the literature, especially in Khuri and Louhichi (Appl Math Lett 82:50-57, 2018).
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics
Uriel Filobello-Nino, Hector Vazquez-Leal, Jesus Huerta-Chua, Jaime Martinez-Castillo, Agustin L. Herrera-May, Mario Alberto Sandoval-Hernandez, Victor Manuel Jimenez-Fernandez
Summary: This work proposes the Enhanced Fixed Point Method (EFPM) as a straightforward modification for solving linear or nonlinear algebraic equations. The method involves modifying the equation using a simple numeric factor, expressing it as a fixed point problem, and employing proposed parameters to accelerate convergence. This method challenges the conventional belief that effective modifications must be lengthy and complicated.
Article
Mathematics, Applied
Tong Li, Jingjing Peng, Zhenyun Peng, Zengao Tang, Yongshen Zhang
Summary: In this paper, a widely used nonlinear matrix equation is discussed, and a fixed-point accelerated iteration method is proposed. The convergence and error estimation of the algorithm are theoretically proved based on the basic characteristics of the Thompson distance. Numerical comparison experiments demonstrate the feasibility and effectiveness of the proposed algorithm.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Operations Research & Management Science
Yair Censor, Daniel Reem, Maroun Zaknoon
Summary: The study presents an extended block-iterative projection method for finding asymptotically a point in the nonempty intersection of a family of closed convex subsets and for handling a family of continuous cutter operators to find a common fixed point. The method is flexible and can handle important specific operators.
JOURNAL OF GLOBAL OPTIMIZATION
(2022)
Article
Materials Science, Multidisciplinary
M. Temmar, B. Michel, I. Ramiere, N. Favrie
JOURNAL OF NUCLEAR MATERIALS
(2020)
Article
Mechanics
Daria Koliesnikova, Isabelle Ramiere, Frederic Lebon
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
(2020)
Article
Engineering, Multidisciplinary
Ye Lu, Thomas Helfer, Benoit Bary, Olivier Fandeur
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Materials Science, Ceramics
Philippe Garcia, Audrey Miard, Thomas Helfer, Jean-Baptiste Parise, Xaviere Iltis, Guy Antou
Summary: Compression test experiments on sintered uranium dioxide at 1500 degrees C reveal initial strain hardening followed by a quasi-steady state period, with stress and oxygen partial pressure exponents estimated in a continuum mechanics framework. SEM/EBSD characterization shows signs of recovery creep and discusses the effect of oxygen pressure on microstructure.
JOURNAL OF THE EUROPEAN CERAMIC SOCIETY
(2021)
Article
Computer Science, Interdisciplinary Applications
Koliesnikova Daria, Ramiere Isabelle, Lebon Frederic
Summary: This paper provides a detailed comparison of adaptive mesh refinement methods for all-quadrilateral and all-hexahedral meshes in a solids mechanics context. The study highlights the potential of locally adaptive multi-grid methods in terms of efficiency metrics.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Chemical
Cristian Camilo Ruiz Vasquez, Noureddine Lebaz, Isabelle Ramiere, Sophie Lalleman, Denis Mangin, Murielle Bertrand
Summary: The present work focuses on the development of a numerical methodology to solve the steady state Population Balance Equation (PBE) for crystallization mechanisms, including nucleation, independent size growth, and loose agglomeration. The methodology is validated and applied to neodymium oxalate precipitation experiments.
CHEMICAL ENGINEERING RESEARCH & DESIGN
(2022)
Article
Materials Science, Multidisciplinary
Tommaso Barani, Isabelle Ramiere, Bruno Michel
Summary: This study presents an engineering-scale model for the migration of porosity in a fuel pellet under a temperature gradient. The model uses a fixed-point iteration technique to solve the system of coupled pore advection and heat diffusion equations. It is tested against benchmark conditions and applied to analyze the contribution of different porosities in fuel restructuring, showing a superior stability compared to a reference model.
JOURNAL OF NUCLEAR MATERIALS
(2022)
Article
Materials Science, Multidisciplinary
C. Introini, J. Sercombe, I. Ramiere, R. Le Tellier
Summary: A phase-field model developed in this paper, combined with a CALPHAD database, is used to simulate incipient melting and oxygen transport in fuel. By directly coupling with the TAF-ID database, the thermodynamic consistency of the model and its capability to simulate the processes are demonstrated.
JOURNAL OF NUCLEAR MATERIALS
(2021)
Article
Mathematics
Simon Le Berre, Isabelle Ramiere, Jules Fauque, David Ryckelynck
Summary: This paper focuses on reduced-order modeling for contact mechanics problems treated by Lagrange multipliers. It discusses the challenges posed by the high nonlinearity of dual solutions and introduces a hyper-reduction approach based on a reduced integration domain (RID). The paper highlights the strong link between the condition number of the projected contact rigidity matrix and the precision of the dual reduced solutions.
Article
Engineering, Multidisciplinary
Daria Koliesnikova, Isabelle Ramiere, Frederic Lebon
Summary: This article proposes an adaptive mesh refinement algorithm for simulating nonlinear quasi-static solid mechanics problems with complex local phenomena. The algorithm provides a fully-automatic, precise, and efficient way to track the evolution of studied phenomena over time. It is based on the multilevel Local Defect Correction refinement approach and addresses open questions related to dynamic mesh adaptation. The proposed algorithm demonstrates effectiveness in various numerical experiments, making it highly valuable for challenging applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics
Louis Belgrand, Isabelle Ramiere, Rodrigue Largenton, Frederic Lebon
Summary: This study focuses on the effects of inclusion proximity on the elastic behavior of dilute matrix-inclusion composites. The results show that the proximity of the inclusions has a significant impact on the elastic properties and stress distributions of the material.
Article
Humanities, Multidisciplinary
Lorenzo Riparbelli, Paola Mazzanti, Thomas Helfer, Chiara Manfriani, Luca Uzielli, Ciro Castelli, Andrea Santacesaria, Luciano Ricciardi, Sandra Rossi, Joseph Gril, Marco Fioravanti
Summary: Wooden Panel Paintings (WPP) are complex objects consisting of a wooden support and pictorial layers that deform over time due to moisture changes. This study conducted hygroscopic tests and sensitivity analysis to understand the variability and complex interactions of input variables on WPP deformation. The results highlighted the need for careful evaluation of uncertainties and interactions in variables to fully comprehend the complexity of the system. The proposed concept of 'learning from objects' integrating experimental investigations and numerical analysis proved essential in characterizing and understanding WPP deformation.
Article
Mechanics
Vincent Gauthier, Renaud Masson, Mihail Garajeu, Thomas Helfer
Summary: In this study, a mean-field micromechanical approach is proposed to determine the effective behavior of a microstructure with damage. The method defines an incremental potential and considers two sub-phases in the damaged phase. The capabilities of the approach are assessed through a specific case and the effective response of the composite is analyzed. The theoretical results compare well with full fields calculations.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Archaeology
L. Riparbelli, P. Dionisi-Vici, P. Mazzanti, F. Bremand, J. C. Dupre, M. Fioravanti, G. Goli, T. Helfer, F. Hesser, D. Jullien, P. Mandron, E. Ravaud, M. Togni, L. Uzielli, E. Badel, J. Gril
Summary: The numerical FEM model was applied to represent the mechanical state of the wooden panel of the Mona Lisa based on non-invasive experimental observations. The model accurately evaluated the strains, stresses, and critical areas of the panel, providing crucial information on its mechanical properties. This study is of great significance for understanding the mechanical condition of the Mona Lisa.
JOURNAL OF CULTURAL HERITAGE
(2023)
Proceedings Paper
Environmental Studies
Dania Koliesnikova, Isabelle Ramiere, Frederic Lebon
Summary: During irradiation in reactors, various phenomena occur at different scales, and it is important to understand and simulate these phenomena accurately over time. The proposed numerical tool based on adaptive mesh refinement techniques and the multilevel Local Defect Correction method is efficient for nonlinear mechanical simulations with evolving local phenomena.
30TH INTERNATIONAL CONFERENCE NUCLEAR ENERGY FOR NEW EUROPE (NENE 2021)
(2021)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)