Article
Computer Science, Interdisciplinary Applications
Nail A. Gumerov, Ramani Duraiswami
Summary: The paper introduces and studies the Green's functions for the Laplace equation on an infinite plane with a circular hole satisfying the Dirichlet and Neumann boundary conditions. These functions enable solutions to boundary value problems in domains with locally rough surfaces, considering arbitrary positive and negative ground elevations. Integral and series representations of the Green's functions are provided, and an efficient computational technique based on the boundary element method with fast multipole acceleration is developed, with numerical studies of benchmark problems presented.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Construction & Building Technology
Arash Tootoonchi, Arman Khoshghalb
Summary: An enriched cell-based smoothed point interpolation method (CSPIM) is proposed for numerical modelling of domains with weak and strong discontinuities, using a triangular background mesh for domain discretisation and enhancement functions near discontinuities. The contact kinematics are satisfied within elements, not at element boundaries, through active set strategy and Coulomb's friction law, simplifying contact algorithm implementation. This method eliminates the need for costly partitioning of elements intersected by discontinuities and is applied to governing equations with a Newton-Raphson scheme for nonlinearities, as demonstrated in two numerical examples.
TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY
(2021)
Article
Computer Science, Interdisciplinary Applications
A. Ortega, E. Roubin, Y. Malecot, L. Daudeville
Summary: This paper analyzes the application of the Embedded Finite Element Method (E-FEM) in simulating local material heterogeneities. It discusses the evolution of weak discontinuity models within the E-FEM framework and establishes a theoretical basis for enhancing weak discontinuities. The paper introduces two enhancement functions and evaluates their performance through numerical simulations.
COMPUTERS & STRUCTURES
(2022)
Article
Engineering, Multidisciplinary
F. Wu, G. Zhou, Q. Y. Gu, Y. B. Chai
Summary: A method called the enriched finite element method (E-FEM) is proposed to enhance the performance and accuracy of solving acoustic problems compared to the traditional finite element method (FEM). By using interpolation cover functions, E-FEM can effectively improve the convergence rate and computational accuracy, as well as suppress dispersion errors at high frequencies.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics
Hassan Chetouani, Nikolaos Limnios
Summary: In this paper, we investigate the weak convergence results for a family of Gibbs measures depending on the parameter theta>0. We prove that the limit distribution is concentrated in the set of global minima of the limit Gibbs potential. Furthermore, we provide an explicit calculation for the limit distribution and apply it to the repairman problem.
Article
Mathematics, Applied
Michael F. Barnsley, P. Viswanathan
Summary: This article discusses the advancement of fractal interpolation functions in various classical nonrecursive methods of approximation. While the focus has been on continuous functions interpolating prescribed data sets, the article introduces the concept of fractal histopolation, which studies the area-matching properties of integrable but not necessarily continuous fractal functions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ashutosh Kumar Karna, Purnima Satapathy
Summary: This article analyzes the well-known Cargo-Leroux model with isentropic perturbation equation of state using the Lie symmetry method, obtaining the corresponding Lie algebra and invariant solutions. Physically significant solutions, such as solitons, are also obtained and demonstrated graphically. Additionally, the hyperbolic nature of the model is examined through the study of evolutionary behavior.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Yingbin Chai, Kangye Huang, Shangpan Wang, Zhichao Xiang, Guanjun Zhang
Summary: The traditional finite element method (FEM) has limitations in solving the Helmholtz equation for large wave numbers due to numerical dispersion errors. This study proposes an extrinsic enriched FEM (EFEM) to overcome this issue and improve the numerical performance. The EFEM enriches the linear approximation space with polynomial and trigonometric functions, effectively capturing the oscillating features of the Helmholtz equation. Numerical examples demonstrate that the EFEM outperforms the standard FEM in controlling dispersion errors and achieves higher convergence rates.
Article
Multidisciplinary Sciences
F. Paquin-Lefebvre, D. Holcman
Summary: This study investigates the diffusion behavior of Brownian particles injected on the surface of a bounded domain, analyzing the distribution of concentration between different windows. The solution is obtained using Green's function techniques and second-order asymptotic analysis, with the results depending on factors such as influx amplitude, diffusion properties, and the geometrical organization of the windows.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics, Applied
Elifalet Lopez-Gonzalez
Summary: The paper focuses on the components of complex analytic functions as solutions to Laplace's equation, and generalizes this result to provide methods for solving other forms of PDEs, including third-order and fourth-order PDEs.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Atiya Perveen, Waleed M. Alfaqih, Salvatore Sessa, Mohammad Imdad
Summary: This paper introduces the concept of theta*-weak contraction to prove fixed point results and respond to open questions raised by Kannan and Rhoades. Illustrative examples are provided to support the results, and the existence and uniqueness of solutions for nonlinear matrix equations and Volterra integral equations are investigated.
Article
Physics, Applied
Bipin Kumar Chaudhary, Randheer Singh
Summary: This study investigates the interaction between a steepened wave and a strong shock in the planar and radially symmetric flow of a van der Waals stiffened relaxing gas. The significance of van der Waals excluded volume, density, and velocity of solid crystals on the steepened wave is determined. Attention is given to analyzing the interaction between the steepened wave and blast wave, and the amplitudes of reflected and transmitted waves as well as the bounce in shock acceleration resulting from the collision between the steepened wave and strong shock are computed.
JOURNAL OF APPLIED PHYSICS
(2023)
Article
Chemistry, Physical
Daniel A. Olaya-Munoz, Juan P. Hernandez-Ortiz, Monica Olvera de la Cruz
Summary: Controlling the aggregation of dielectric particles can be achieved by adjusting their geometry and contact surface.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Engineering, Geological
Timo Saksala
Summary: This study investigates the influence of initial microcracks on the fracture behavior of natural rocks through numerical simulations of uniaxial tension and three-point bending tests. The findings show that the strength lowering effect of initial microcrack populations is more pronounced under uniaxial tension compared to three-point bending.
Article
Engineering, Multidisciplinary
Li-Ping Zhang, Zi-Cai Li, Hung-Tsai Huang, Ming-Gong Lee
Summary: This paper investigates the Dirichlet problem for Laplace's/Poisson's equation in a bounded simply-connected domain, exploring the singularity of the solution and deriving reduced convergence rates. New removal techniques are proposed and validated through numerical experiments.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mathematics, Applied
Guo Zheng, Zengqiang Cao, Yuehaoxuan Wang, Reza Talemi
Summary: This study introduces two novel methods for predicting the fatigue response of Dynamic Cold Expansion (DCE) and Static Cold Expansion (SCE) open-hole plates. The accuracy of the prediction is enhanced by considering stress distributions and improving existing methods. The study also discusses the mechanisms behind fatigue life enhancement and fatigue crack propagation modes in cold expansion specimens.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Eric Heppner, Tomohiro Sasaki, Frank Trommer, Elmar Woschke
Summary: This paper presents a modeling approach for estimating the bonding strength of friction-welded lightweight structures. Through experiments and simulations, a method for evaluating the bonding strength of friction-welded lightweight structures is developed, and the plausibility and applicability of the model are discussed.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Piermario Vitullo, Alessio Colombo, Nicola Rares Franco, Andrea Manzoni, Paolo Zunino
Summary: Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to capture fine details at small scales. Traditional projection based reduced order models (ROMs) fail to resolve these issues, even for second-order elliptic PDEs commonly found in engineering applications. To address this, we propose an alternative nonintrusive strategy to build a ROM, that combines classical proper orthogonal decomposition (POD) with a suitable neural network (NN) model to account for the small scales.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Chanh Dinh Vuong, Xiaofei Hu, Tinh Quoc Bui
Summary: In this paper, we present a dynamic description of the smoothing gradient-enhanced damage model for the simulation of quasi-brittle failure localization under time-dependent loading conditions. We introduce two efficient rate-dependent damage laws and various equivalent strain formulations to analyze the complicated stress states and inertia effects of the dynamic regime, enhancing the capability of the adopted approach in modeling dynamic fracture and branching.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Alexandre D. C. Amaro, A. Francisca Carvalho Alves, F. M. Andrade Pires
Summary: This study focuses on analyzing various deformation mechanisms that affect the behavior of PC/ABS blends using computational homogenization. By establishing a representative microstructural volume element, defining the constitutive description of the material phases, and modeling the interfaces and matrix damage, accurate predictions can be achieved. The findings have important implications for broader applications beyond PC/ABS blends.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
David Hoffmeyer, A. R. Damanpack
Summary: This paper introduces a method for determining all six stress components for a cantilever-type beam that is subjected to concentrated end loads. The method considers an inhomogeneous cross-section and employs cylindrically orthotropic material properties. The efficacy of the method is validated by numerical examples and a benchmark example, and the analysis on a real sawn timber cross-section reveals significant disparities in the maximum stresses compared to conventional engineering approaches.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Vladimir Stojanovic, Jian Deng, Dunja Milic, Marko D. Petkovic
Summary: The present paper investigates the dynamic analysis of a coupled Timoshenko beam-beam or beam-arch mechanical system with geometric nonlinearities. A modified p-version finite element method is developed for the vibrations of a shear deformable coupled beam system with a discontinuity in an elastic layer. The main contribution of this work is the discovery of coupled effects and phenomena in the simultaneous vibration analysis of varying discontinuity and varying curvature of the newly modelled coupled mechanical system. The analysis results are valuable and have broader applications in the field of solids and structures.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Gihwan Kim, Phill-Seung Lee
Summary: The phantom-node method is applied in the phase field model for mesh coarsening to improve computational efficiency. By recovering the fine mesh in the crack path domain into a coarse mesh, this method significantly reduces the number of degrees of freedom involved in the computation.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Souhail Chaouch, Julien Yvonnet
Summary: In this study, an unsupervised machine learning-based clustering approach is developed to reduce the computational cost of nonlinear multiscale methods. The approach clusters macro Gauss points based on their mechanical states, reducing the problem from macro scale to micro scale. A single micro nonlinear Representative Volume Element (RVE) calculation is performed for each cluster, using a linear approximation of the macro stress. Anelastic macro strains are used to handle internal variables. The technique is applied to nonlinear hyperelastic, viscoelastic and elastoplastic composites.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Hoang-Giang Bui, Jelena Ninic, Christian Koch, Klaus Hackl, Guenther Meschke
Summary: With the increasing demand for underground transport infrastructures, it is crucial to develop methods and tools that efficiently explore design options and minimize risks to the environment. This study proposes a BIM-based approach that connects user-friendly software with effective simulation tools to analyze complex tunnel structures. The results show that modeling efforts and computational time can be significantly reduced while maintaining high accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Aslan Nasirov, Xiaoyu Zhang, David Wagner, Saikumar R. Yeratapally, Caglar Oskay
Summary: This manuscript presents an efficient model construction strategy for the eigenstrain homogenization method (EHM) for the reduced order models of the nonlinear response of heterogeneous microstructures. The strategy relies on a parallel, element-by-element, conjugate gradient solver, achieving near linear scaling with respect to the number of degrees of freedom used to resolve the microstructure. The linear scaling in the number of pre-analyses required to construct the reduced order model (ROM) follows from the EHM formulation. The developed framework has been verified using an additively manufactured polycrystalline microstructure of Inconel 625.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Atticus Beachy, Harok Bae, Jose A. Camberos, Ramana V. Grandhi
Summary: Emulator embedded neural networks leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. However, training the ensemble models can be costly and pose computational challenges. This work presents a new type of emulator embedded neural network using the rapid neural network paradigm, which trains near-instantaneously without loss of prediction accuracy.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Arash Hajisharifi, Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: This paper introduces three reduced order models for reducing computational time in atmospheric flow simulation while preserving accuracy. Among them, the PODI method, which uses interpolation with radial basis functions, maintains accuracy at any time interval.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
D. Munoz, S. Torregrosa, O. Allix, F. Chinesta
Summary: The Proper Generalized Decomposition (PGD) is a Model Order Reduction framework used for parametric analysis of physical problems. It allows for offline computation and real-time simulation in various situations. However, its efficiency may decrease when the domain itself is considered as a parameter. Optimal transport techniques have shown exceptional performance in interpolating fields over geometric domains with varying shapes. Therefore, combining these two techniques is a natural choice. PGD handles the parametric solution while the optimal transport-based methodology transports the solution for a family of domains defined by geometric parameters.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)
Article
Mathematics, Applied
Jothi Mani Thondiraj, Akhshaya Paranikumar, Devesh Tiwari, Daniel Paquet, Pritam Chakraborty
Summary: This study develops a diffused interface CPFEM framework, which reduces computational cost by using biased mesh and provides accurate results using non-conformal elements in the mesh size transiting regions. The accuracy of the framework is confirmed through comparisons with sharp and stepped interface results.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2024)