Article
Physics, Mathematical
Ang Li, Hongtao Yang, Yonghai Li, Guangwei Yuan
Summary: In this paper, we correct the finite volume element methods for diffusion equations on general triangular and quadrilateral meshes. By decomposing the numerical fluxes and introducing local extremums, we obtained nonlinear numerical fluxes that satisfy the discrete strong extremum principle, while preserving the convergence order.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2022)
Article
Physics, Mathematical
Chris Schoutrop, Jan ten Thije Boonkkamp, Jan van Dijk
Summary: This study investigates the reliability of BiCGStab and IDR solvers for the exponential scheme discretization of the advection-diffusion-reaction equation. It is shown that the benefit of BiCGStab(L) compared to BiCGStab is modest in numerical experiments, and non-sparse shadow residual is essential for the reliability of BiCGStab. The reliable updating scheme ensures the required tolerance is truly achieved. IDR(S) outperforms BiCGStab for problems with strong advection in terms of the number of matrix-vector products.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2022)
Article
Environmental Sciences
Zehao Chen, Hongbin Zhan
Summary: This study investigates how transport properties affect contaminant transport in a multi-layer porous media system through high-resolution finite-element numerical models. The results show that porosity and retardation factor have similar impacts on the mass flux across layer interfaces, while increasing the transverse dispersivity enhances the mass flux between layers. The study has important implications for managing contaminant remediation in layered aquifers.
Article
Mathematics, Applied
Zhilin Li, Kejia Pan
Summary: In this paper, new fourth order compact schemes for Robin and Neumann boundary conditions are developed for boundary value problems of elliptic PDEs in two and three dimensions. These schemes utilize carefully designed undetermined coefficient methods and can be applied to various elliptic PDEs including both flux and linear boundary conditions. The developed schemes are versatile and generally have M-matrices as coefficient matrices, ensuring well-posed problems and convergence of the methods. Examples with large wave numbers and oscillatory solutions are presented to demonstrate the performance of the new schemes.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Environmental Sciences
Tian Jiao, Ming Ye, Menggui Jin, Jing Yang
Summary: The Smoothed Particle Hydrodynamics (SPH) method is a Lagrangian approach widely used for solving numerical dispersion problems in groundwater solute transport. To improve accuracy in models with irregular particle distribution, an Interactively Corrected SPH (IC-SPH) method was developed. IC-SPH uses interactively corrected kernel gradients to construct concentration gradients, resulting in more accurate and faster converging solutions.
WATER RESOURCES RESEARCH
(2022)
Article
Environmental Sciences
Seyed Taleb Hosseini, Emil Stanev, Johannes Pein, Arnoldo Valle-Levinson, Corinna Schrum
Summary: This study compares the influences of density gradient and tides in funnel-shaped salt-plug estuaries, and examines the longitudinal and lateral circulations using a three-dimensional numerical model. The results show positive longitudinal estuarine circulation landward of the salt plug and inverse circulation seaward of the salt plug. The salt plug is saltier during spring tides due to higher landward salt transport. The lateral circulation shows neap-spring variability and reverses direction in the salt-plug area. A threshold condition for salt-plug estuaries is introduced, where tidal forcing can overcome density gradient and reinforce salinity inside the salt plug zone.
FRONTIERS IN MARINE SCIENCE
(2023)
Article
Engineering, Multidisciplinary
Roberto J. Cier, Sergio Rojas, Victor M. Calo
Summary: The translated text describes a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptivity. The method efficiently demonstrates high applicability in various engineering applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Marcio Batista, Henrique F. de Lima
Summary: In this paper, we investigate the translation solitons of mean curvature flow in specific product spaces. Assuming certain conditions on volume growth or scalar curvature growth, we establish a maximum principle for the drift Laplacian and derive nonexistence results. Furthermore, we examine the case where a smooth function u determines an entire translating graph over the base of a product space and apply a Bernstein type result to prove the constancy of u. This leads to the nonexistence of entire solutions for quasilinear partial differential equations related to translating graphs.
RESULTS IN MATHEMATICS
(2023)
Article
Mathematics, Applied
Andreas Rupp, Moritz Hauck, Vadym Aizinger
Summary: The method introduced in this work generalizes the enriched Galerkin method with an adaptive two-mesh approach, proving stability and error estimates for a linear advection equation. The analysis technique allows for arbitrary degrees of enrichment on both coarse and fine meshes, covering a wide range of methods from continuous finite element to discontinuous Galerkin with local subcell enrichment. Numerical experiments confirm the analytical results and show good robustness of the proposed method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Civil
Yulong Gao, Shuping Yi, Chunmiao Zheng
Summary: Groundwater solute transport models are critical for simulating subsurface contaminant processes, guiding policy making, and pollution remediation. The improved model developed in this study demonstrates efficient simulation of solutes in complex boundary aquifer systems, with better performance compared to conventional models in real-world watersheds. This model offers robust solutions for simulating groundwater solute transport processes, particularly in aquifer systems with complex shaped boundaries, and provides a flexible discretization solution for coupling surface water models.
JOURNAL OF HYDROLOGY
(2021)
Article
Mathematics, Applied
Rodolfo Bermejo, Jaime Carpio, Laura Saavedra
Summary: In this paper, we study new developments of the Lagrange-Galerkin method for the advection equation. The first part of the article presents a new improved error estimate of the conventional Lagrange-Galerkin method. The second part introduces a new local projection stabilized Lagrange-Galerkin method, while the third part introduces and analyzes a discontinuity-capturing Lagrange-Galerkin method. Additionally, numerical experiments are conducted to investigate the influence of quadrature rules on the stability and accuracy of the methods.
Article
Computer Science, Interdisciplinary Applications
Sergii Kivva
Summary: This paper introduces a novel method for designing flux correction in weighted hybrid difference schemes using linear programming. By applying inequalities from the monotone difference scheme to the hybrid scheme, the determination of maximal antidiffusive fluxes is treated as a linear optimization problem, which is then simplified to an iterative solution of linear programming problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Mohammad Partohaghighi, Marzieh Mortezaee, Ali Akgul, Sayed M. Eldin
Summary: Transport of contaminants is a crucial environmental issue, and accurate modeling is vital for effective management strategies. This study introduces a non-integer model for the advection-dispersion problem in contaminant transport. The numerical solution is obtained using discrete Chebyshev polynomials and an operational matrix. The suggested scheme is validated through comparison with other numerical methods.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Shuai Wang, Guangwei Yuan
Summary: This paper introduces a nonlinear correction technique for finite element methods to solve anisotropic diffusion problems on general triangular and quadrilateral meshes. The classic linear or bi-linear finite element methods are modified to satisfy the discrete strong extremum principle unconditionally, eliminating the need for known restrictions on diffusion coefficients and mesh-cell geometry (such as acute angle condition). The convergence rate for smooth and piecewise smooth solutions and the property of discrete extremum principle are verified through numerical examples.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Jundong Feng, Yingcong Zhou, Tianliang Hou
Summary: In this paper, a new linear second-order finite difference scheme for Allen-Cahn equations is proposed, with stability and discrete maximum principle. Numerical experiments validate the theoretical results.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Remi Abgrall, Elise Le Meledo, Philipp Offner
Summary: The research introduces a class of discretization spaces and H(div)-conformal elements that can be applied to any polytope, combining flexibility of Virtual Element spaces with divergence properties of Raviart-Thomas elements. This design allows for a wide range of H(div)-conformal discretizations, easily adaptable to desired properties of approximated quantities. Additionally, a specific restriction of this general setting shows properties similar to classical Raviart-Thomas elements at each interface, for any order and polytopal shape.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2021)
Article
Computer Science, Interdisciplinary Applications
Ronit Kumar, Lidong Cheng, Yunong Xiong, Bin Xie, Remi Abgrall, Feng Xiao
Summary: The THINC-scaling scheme unifies the VOF and level set methods by maintaining a high-quality reconstruction function, preserving the advantages of both methods, and allowing representation of interfaces with high-order polynomials. The scheme provides high-fidelity solutions comparable to other advanced methods and can resolve sub-grid filament structures if the interface is represented by a polynomial higher than second order.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Sixtine Michel, Davide Torlo, Mario Ricchiuto, Remi Abgrall
Summary: The paper studies continuous finite element dicretizations for one dimensional hyperbolic partial differential equations, providing a fully discrete spectral analysis and suggesting optimal values of the CFL number and stabilization parameters. Different choices for finite element space and time stepping strategies are compared to determine the most promising combinations for accuracy and stability, with suggestions for optimal discretization parameters.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Jianfang Lin, Yupeng Ren, Remi Abgrall, Jianxian Qiu
Summary: In this paper, a high order residual distribution (RD) method is developed for solving steady state conservation laws using a novel Hermite weighted essentially non-oscillatory (HWENO) framework. The proposed method has advantages in terms of computational efficiency and accuracy compared to traditional methods. Extensive numerical experiments confirm the high order accuracy and good quality of the scheme.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Paola Bacigaluppi, Julien Carlier, Marica Pelanti, Pietro Marco Congedo, Remi Abgrall
Summary: This work presents the formulation of a four-equation model for simulating unsteady two-phase mixtures with phase transition and strong discontinuities. The proposed method uses a non-conservative formulation to avoid oscillations obtained by many approaches and relies on a finite element based residual distribution scheme.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Barbara Re, Remi Abgrall
Summary: Within the framework of diffuse interface methods, a pressure-based Baer-Nunziato type model is derived for weakly compressible multiphase flows. The model can handle different equations of state and includes relaxation terms characterized by user-defined finite parameters. The solution strategy involves a semi-implicit finite-volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. The developed simulation tool is validated through various tests, showing good agreement with analytical and reference results.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2022)
Article
Computer Science, Interdisciplinary Applications
Remi Abgrall, Philipp Oeffner, Hendrik Ranocha
Summary: This paper proposes an approach to construct entropy conservative/dissipative semidiscretizations in the general class of residual distribution (RD) schemes. The approach involves adding suitable correction terms characterized as solutions of certain optimization problems. The method is applied to the SBP- SAT framework and novel generalizations to entropy inequalities, multiple constraints, and kinetic energy preservation for the Euler equations are developed. Explicit solutions are provided for all optimization problems, and a fully discrete entropy conservative/dissipative RD scheme is obtained using the deferred correction method for time integration.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Remi Abgrall, Fatemeh Nassajian Mojarrad
Summary: This paper presents schemes for the compressible Euler equations that focus on conserving angular momentum locally. A general framework is proposed, examples of schemes are described, and results are shown. These schemes can be of arbitrary order.
COMPUTERS & FLUIDS
(2022)
Article
Computer Science, Interdisciplinary Applications
Remi Abgrall, Pratik Rai, Florent Renac
Summary: In this work, a discretization method for simulating compressible multicomponent flows with shocks and material interfaces is proposed. The method is accurate, robust, and stable. By modifying the integrals over discretization elements, a scheme with a HLLC solver is designed to preserve material interfaces and satisfy minimum and maximum principles of entropy. Numerical experiments validate the stability, robustness, and accuracy of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Sixtine Michel, Davide Torlo, Mario Ricchiuto, Remi Abgrall
Summary: This study investigates various continuous finite element discretization methods for two-dimensional hyperbolic partial differential equations. The schemes are ranked based on efficiency, stability, and dispersion error, and the best CFL and stabilization coefficients are provided. Challenges in two dimensions include Fourier analysis and the introduction of high-order viscosity. The results suggest that combining Cubature elements with SSPRK and OSS stabilization yields the most promising combination.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Remi Abgrall, Saray Busto, Michael Dumbser
Summary: We present a simple and general framework for constructing thermodynamically compatible schemes for overdetermined hyperbolic PDE systems. The proposed algorithms solve the entropy inequality as a primary evolution equation, leading to total energy conservation as a consequence of the compatible discretization. We apply the framework to the construction of three different numerical methods and demonstrate their stability and accuracy through numerical experiments.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Remi Abgrall, Fatemeh Nassajian Mojarrad
Summary: We propose a class of fully explicit kinetic numerical methods in compressible fluid dynamics, which can achieve arbitrarily high order in both time and space. These methods, including the relaxation schemes by Jin and Xin, allow for the use of CFL number larger or equal to unity on regular Cartesian meshes for multi-dimensional problems. The methods depend on a small parameter that represents a Knudsen number and are asymptotic preserving in this parameter. The computational costs of the methods are comparable to fully explicit schemes. The extension of these methods to multi-dimensional systems has been assessed and proven to be robust and achieve the theoretically predicted high order of accuracy on smooth solutions.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
R. Abgrall
Summary: This article demonstrates a way to combine the conservative and non-conservative formulations of a hyperbolic system that has a conservative form. The solution is described using a combination of point values and average values, with different meanings for point-wise and cell average degrees of freedom. The article also presents a new method for nonlinear stability and provides results from various benchmark tests.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Remi Abgrall, Davide Torlo
Summary: This paper describes a method for constructing arbitrarily high order kinetic schemes on regular meshes and introduces a nonlinear stability method for simulating problems with discontinuities without sacrificing accuracy for smooth regular solutions.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2022)
Article
Mathematics, Applied
R. Abgrall, J. Nordstrom, P. Oeffner, S. Tokareva
JOURNAL OF SCIENTIFIC COMPUTING
(2020)
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)