Article
Mathematics, Applied
Derk Frerichs, Volker John
Summary: This paper studies post-processing methods to reduce spurious oscillations in discontinuous Galerkin finite element method, which involve replacing the DG solution near layers with constant or linear approximations. Numerical studies confirm the effectiveness of these post-processing methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Derk Frerichs-Mihov, Volker John
Summary: This note investigates a generalization of a post-processing technique and a novel method inspired by the same technique, which effectively reduce spurious oscillations in discontinuous Galerkin solutions of convection-diffusion equations in the convection-dominated regime.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Nancy Chalhoub, Pascal Omnes, Toni Sayah, Rebecca El Zahlaniyeh
Summary: This article investigates the time-dependent convection-diffusion-reaction equation coupled with the Darcy equation. A numerical scheme based on finite element methods and the implicit Euler method is proposed, and optimal a posteriori error estimates with computable error indicators are established. Numerical investigations confirm the theoretical results.
NUMERICAL ALGORITHMS
(2022)
Article
Mathematics, Applied
Derk Frerichs-Mihov, Linus Henning, Volker John
Summary: This paper studies the application of deep neural networks for detecting mesh cells on which slope limiters should be applied. The networks are trained with data obtained from simulations of a standard benchmark problem with linear finite elements. It is investigated how they perform when applied to discrete solutions obtained with higher order finite elements and to solutions for a different benchmark problem.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
Albert Puigferrat, Miguel Maso, Ignasi De-Pouplana, Guillermo Casas, Eugenio Onate
Summary: A numerical method combining Lagrangian and Eulerian approaches is proposed to solve advective-diffusive-absorptive problems, showing effectiveness through validation with various test cases.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Reza Doostaki, Mohammad Mehdi Hosseini, Abbas Salemi
Summary: This paper presents a new compact finite difference scheme for solving linear high-dimensional time-dependent partial differential equations (PDEs). The proposed method achieves arbitrary order accuracy in both time and space, and obtains the approximation of partial derivatives simultaneously at all grid points. The numerical results demonstrate the accuracy and efficiency of the proposed method by solving parabolic and convection-diffusion equations with fourth, sixth, and eighth-order simultaneously compact finite difference schemes.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Troy Shilt, Patrick J. O'Hara, Jack J. McNamara
Summary: The article explores the alleviation of spurious oscillations introduced by traditional finite element methods in advection dominated problems through a generalized finite element formulation. This method is demonstrated to effectively capture boundary layer development and provide smooth numerical solutions with improved error levels compared to traditional formulations. Insights into the improvements offered by the generalized finite element method are further illuminated through a consistent decomposition of the variational multiscale method for comparison with classical stabilized methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Aleksandr Romanov
Summary: This study focuses on dissipative reaction-diffusion-convection systems on the circle and identifies conditions under which the final phase dynamics can be described by an ODE with Lipschitz vector field in R-N. A recent construction of a parabolic problem in mathematical physics within this class lacks the indicated property.
Article
Mathematics, Applied
Xiaobing Feng, Yan Luo, Liet Vo, Zhu Wang
Summary: This paper develops a general iterative framework for solving parameter-dependent and random convection-diffusion problems, which allows for significant computation saving. The proposed method reformulates the underlying problem and employs a fixed-point iteration to compute the solution, achieving convergence and rates of convergence.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Yujie Liu, Junping Wang
Summary: An extended P-1 nonconforming finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations on general polytopal partitions, inspired by the simplified weak Galerkin method. The method reduces computational complexity by utilizing only the degrees of freedom on the boundary of each element. Numerical stability and optimal order of error estimates in H-1 and L-2 norms are established for the numerical solutions, with a superconvergence phenomenon noted on rectangular partitions through numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Antoine Tambue, Jean Daniel Mukam
Summary: This paper investigates the numerical approximation of stochastic convection-reaction-diffusion equations using two explicit exponential integrators, achieving higher convergence orders with the construction of accelerated numerical methods. Numerical experiments are provided to illustrate the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Construction & Building Technology
Albert Puigferrat, Ignasi De-Pouplana, Fulvio Amato, Onate Eugenio
Summary: This study presents a procedure for coupling fluid and transport equations to model pollutant distribution in a street canyon, focusing on black carbon (BC). The method utilizes two approaches implemented on the KRATOS platform, aiming to provide a useful tool for studying pollution effects on pedestrians with good comparison to experimental results.
BUILDING AND ENVIRONMENT
(2021)
Article
Mathematics, Applied
Chunmei Wang, Ludmil Zikatanov
Summary: The paper discusses finite element discretizations for convection-diffusion problems under low regularity assumptions, using the primal-dual weak Galerkin (PDWG) finite element framework. The proposed PDWG method is proven to be stable and convergent, with a priori error estimates derived for the primal variable. Numerical tests validate the theory presented in the study.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Hamza Ammar, Moncef Mahjoub, Nejib Zemzemi
Summary: In this paper, the authors investigate an inverse problem in cardiac electrophysiology modeling, where two space dependent ionic parameters of a reaction-diffusion system are determined using multi-electrode array/human induced pluripotent stem cells-cardiomyocytes assays to simulate drug action. The bidomain model coupled with an ordinary differential equation is used, and the FitzHugh-Nagumo phenomenological model is employed to describe ionic exchanges at the microscopic level. The main result of the paper is the uniqueness and Lipschitz stability estimate for the two ionic parameters, achieved through sub-boundary observations over a time interval. The key components include global Carleman-type estimates and suitable observations on a part of the boundary.
Article
Computer Science, Interdisciplinary Applications
Chuwen Ma, Weiying Zheng
Summary: A fourth-order unfitted characteristic finite element method is proposed for solving free-boundary problems of time-dependent partial differential equations. The method utilizes a fourth-order forward flow map and a fourth-order backward flow map to track the domain and discretize the PDE, providing a framework for designing high-order numerical methods. Extensive numerical experiments confirm the effectiveness and accuracy of the method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)