Article
Mathematics, Applied
Felipe Lepe, Jesus Vellojin
Summary: In this paper, we design and analyze a posteriori error estimators for the mixed Stokes eigenvalue problem in two and three dimensions. The unknowns in this mixed formulation are the pseudotress, velocity, and pressure. Using a lowest order mixed finite element scheme and a postprocessing technique, we prove the reliability and efficiency of the proposed estimator. Numerical tests in two and three dimensions are conducted to assess the performance of the estimator.
Article
Mathematics, Applied
Pierre-Henri Cocquet, Michael Rakotobe, Delphine Ramalingom, Alain Bastide
Summary: This paper deals with the finite element approximation of the Darcy-Brinkman-Forchheimer equation for porous media with spatially-varying porosity and mixed boundary conditions. It proves uniqueness of the solution under certain conditions and convergence of the finite element approximation. Numerical experiments are provided to illustrate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Felipe Lepe, Gonzalo Rivera, Jesus Vellojin
Summary: In this paper, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The methods approximate the velocity and pressure with piecewise polynomials, and use the Raviart-Thomas and Brezzi-Douglas-Marini elements to approximate the pseudostress. By utilizing the classic spectral theory for compact operators, we prove that our method does not introduce spurious modes and obtain convergence and error estimates. Numerical results are presented to compare the accuracy and robustness of both numerical schemes.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Felipe Lepe, Gonzalo Rivera, Jesus Vellojin
Summary: The aim of this paper is to analyze a mixed formulation for the two dimensional Stokes eigenvalue problem, where the stress and velocity are the unknowns and the pressure can be recovered through postprocessing. The paper proposes a mixed numerical method using suitable finite elements for stress approximation and piecewise polynomials for velocity approximation. Convergence and spectral correctness of the proposed method are derived using compact operators theory. Additionally, a reliable and efficient a posteriori error estimator is proposed for achieving optimal convergence order in the presence of non-sufficient smooth eigenfunctions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Lingling Sun, Yidu Yang
Summary: This paper discusses the a posteriori error estimates and adaptive algorithm of non-conforming mixed finite elements for the Stokes eigenvalue problem. The reliability and efficiency of the error estimators are proven. Two adaptive algorithms, direct AFEM and shifted-inverse AFEM, are built based on the error estimators. Numerical experiments and theoretical analysis show that the numerical eigenvalues obtained by these algorithms achieve optimal convergence order and approximate the exact solutions from below.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Engineering, Multidisciplinary
Lady Angelo, Jessika Camano, Sergio Caucao
Summary: In this paper, a new mixed variational formulation for a stationary magnetohydrodynamic flows in porous media problem is introduced and analyzed. The resulting mixed scheme is proven to be stable, convergent, and optimal a priori error estimates are obtained. Numerical tests are conducted to validate the theoretical results.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Maria Gonzalez, Magdalena Strugaru
Summary: This study introduces a new augmented dual-mixed finite element method for solving the linear convection-diffusion equation with mixed boundary conditions. The research proves that the new variational formulation and the corresponding Galerkin scheme are well-posed with appropriate parameter settings, and a Cea estimate can be derived. Additionally, convergence rates for approximating flux and concentration are established using different methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Francisco Fuica, Felipe Lepe, Enrique Otarola, Daniel Quero
Summary: In this study, error estimators for the Stokes system with singular sources in suitable function spaces were designed and analyzed. The error estimators were proven to be reliable and locally efficient in Lipschitz polytopal domains. Based on these estimators, a simple adaptive strategy was developed that achieved optimal rates of convergence in numerical experiments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Automation & Control Systems
Alejandro Allendes, Francisco Fuica, Enrique Otarola, Daniel Quero
Summary: In this study, a posteriori error estimators for an optimal control problem involving the stationary Navier-Stokes equations are proposed and analyzed in Lipschitz, non-convex polytopal domains. Two discretization strategies are devised and proven to be reliable, with exploration of local efficiency estimates. Numerical experiments demonstrate competitive performance of adaptive loops based on the devised error estimators.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Weimin Han, Kenneth Czuprynski, Feifei Jing
Summary: This paper develops and studies a mixed finite element method for solving the NS hemivariational inequality. The method is used to explore solution existence and uniqueness, with numerical results reported using the P1b/P1 pair. The error analysis predicts optimal convergence order.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Hui Peng, Qilong Zhai, Ran Zhang, Shangyou Zhang
Summary: This paper proposes a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition, and validates the theoretical analysis through numerical experiments.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics, Applied
Sergio Caucao, Gabriel N. Gatica, Ricardo Oyarzua, Paulo Zuniga
Summary: This paper considers the coupling problem of the stationary Brinkman-Forchheimer and double-diffusion equations and develops an a posteriori error analysis for the associated mixed finite element scheme. Two reliable and efficient residual-based error estimators are derived, ensuring the reliability and efficiency of the estimators on arbitrary regions.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Yanren Hou, Dandan Xue
Summary: This paper investigates a two-grid decoupling finite element scheme for the mixed Navier-Stokes/Darcy model with Beavers-Joseph-Saffman's interface condition and establishes the optimal error estimate for the approximate solution. The analysis shows that the fine grid decoupled problems, i.e., the Navier-Stokes equations and the Darcy equation, can be solved simultaneously and achieve the optimal convergence order.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Toni Sayah
Summary: This paper investigates the a posteriori error estimate for the Brinkman-Darcy-Forchheimer problem, introducing the variational formulation discretized using the finite element method, establishing an a posteriori error estimation with two types of error indicators related to discretization and linearization, and presenting and discussing numerical investigations.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Alejandro Allendes, Gilberto Campana, Enrique Otarola
Summary: In this paper, we study a Darcy-Forchheimer problem coupled with a singular heat equation in Lipschitz domains, where the nonlinear forcing term depends on the temperature. We establish the existence of solutions for a model that allows the diffusion coefficient in the heat equation to depend on the temperature. Additionally, we propose a finite element discretization scheme and provide a convergence analysis. When the diffusion coefficient is constant, we devise an a posteriori error estimator and investigate reliability and efficiency properties. Finally, we devise an adaptive loop based on the proposed error estimator and present numerical experiments.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Jessika Camano, Sergio Caucao, Ricardo Oyarzua, Segundo Villa-Fuentes
Summary: In this paper, a new momentum conservative mixed finite element method is developed for solving the steady-state Navier-Stokes problem in two and three dimensions, and an a posteriori error analysis is conducted. By extending standard techniques from Hilbert spaces to Banach spaces, a reliable and efficient residual-based a posteriori error estimator is derived for the mixed finite element scheme on arbitrary polygonal and polyhedral regions. The efficiency of the proposed error indicator is proven using inverse inequalities and the localization technique based on bubble functions.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Ricardo Ruiz-Baier, Matteo Taffetani, Hans D. Westermeyer, Ivan Yotov
Summary: In this study, a new mixed-primal finite element scheme was proposed to solve the multiphysics model involving fluid flow and consolidation equations without the need for Lagrange multipliers. The research focused on numerical simulations related to geophysical flows and eye poromechanics, exploring different interfacial flow regimes that could help understand early morphologic changes associated with glaucoma in canine species.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
J. Querales, P. Venegas
Summary: This paper studies the numerical approximation of mixed formulations for the acoustic eigenvalue problem with axial symmetry and introduces two mixed formulations to avoid spurious modes. The proposed method based on the Raviart-Thomas mixed method is analyzed and shown to have convergence and quasi-optimal order error estimates, which are supported by numerical results.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
A. Bermudez, B. Lopez-Rodriguez, F. J. Pena, R. Rodriguez, P. Salgado, P. Venegas
Summary: This paper focuses on the numerical approximation of an axisymmetric time-harmonic eddy current problem involving an in-plane current. It discusses the existence and uniqueness of solutions, convergence results, error estimates, and numerical results confirming theoretical estimates. The proposed method successfully computes the current density distribution in a steel cylindrical bar subjected to electric-upsetting.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Ana Alonso-Rodriguez, Jessika Camano, Eduardo De Los Santos, Rodolfo Rodriguez
Summary: In this paper, a divergence-free finite element method for solving a fluid-structure interaction spectral problem in three dimensions is analyzed. The method accurately approximates the eigenvalues and eigenfunctions using appropriate basis functions and has been demonstrated to perform well through numerical results.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Gabriel N. Gatica, Bryan Gomez-Vargas, Ricardo Ruiz-Baier
Summary: In this paper, the a posteriori error analysis for mixed-primal and fully-mixed finite element methods approximating the stress-assisted diffusion of solutes in elastic materials is developed. Two efficient and reliable residual-based a posteriori error estimators are derived and their performance is confirmed through numerical tests, illustrating the effectiveness of adaptive mesh refinement.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
N. A. Barnafi, B. Gomez-Vargas, W. J. Lourenco, R. F. Reis, B. M. Rocha, M. Lobosco, R. Ruiz-Baier, R. Weber dos Santos
Summary: In this paper, we propose a novel coupled poroelasticity-diffusion model that considers the formation process of extracellular edema and infectious myocarditis under large deformations. The model takes into account the interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. A numerical approximation scheme using five-field finite element method is developed and stability analysis is conducted. The computational tests demonstrate the properties of the model and finite element schemes.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Veronica Anaya, Arbaz Khan, David Mora, Ricardo Ruiz-Baier
Summary: We develop the a posteriori error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. Our methods are robust and valid in 2D and 3D, and for arbitrary polynomial degree. Numerical examples demonstrate the error behavior predicted by the theoretical analysis, and adaptive mesh refinement is performed based on the a posteriori error estimators.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Physiology
Wesley de Jesus Lourenco, Ruy Freitas Reis, Ricardo Ruiz-Baier, Bernardo Martins Rocha, Rodrigo Weber dos Santos, Marcelo Lobosco
Summary: This paper investigates the formation of myocardial edema in acute infectious myocarditis and modifies a model to describe the associated dynamics. Computational methods can provide insights into the relationship between pathogens and the immune system, shedding light on the variations in myocarditis inflammation among different patients.
FRONTIERS IN PHYSIOLOGY
(2022)
Article
Computer Science, Interdisciplinary Applications
Wietse M. Boon, Martin Hornkjol, Miroslav Kuchta, Kent-Andre Mardal, Ricardo Ruiz-Baier
Summary: This paper advances the analysis of discretizations for a fluid-structure interaction model, proposing a five-field mixed-primal finite element scheme and deriving adequate inf-sup conditions. The stability of the formulation is established robustly in all material parameters and its performance is corroborated by several test cases.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Sergio Caucao, Ricardo Oyarzua, Segundo Villa-Fuentes
Summary: In this paper, a new mixed finite element scheme for the Boussinesq model describing natural convection is studied. A reliable and efficient residual-based a posteriori error estimator for the corresponding Galerkin scheme is derived. By extending standard techniques commonly used on Hilbert spaces to the case of Banach spaces, the error estimator is obtained on arbitrary polygonal and polyhedral regions. The local efficiency of the proposed estimator is proven using inverse inequalities, the localization technique based on bubble functions, and known results from previous works.
Article
Mathematics, Applied
Jessika Camano, Carlos Garcia, Ricardo Oyarzua
Summary: This paper proposes and analyzes a new mixed finite element method for solving the stationary magneto-hydrodynamic (MHD) model. The method combines a dual-mixed formulation for the Navier-Stokes problem with a classical primal formulation for the Maxwell equations. The analysis of the continuous and discrete problems is carried out using mathematical theorems, and an a priori error analysis is provided. The numerical results demonstrate the effectiveness of the proposed method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
A. Alonso Rodriguez, J. Camano
Summary: We analyze a new algorithm that approximates eigenvalue problems for the curl operator, including the helicity of a bounded domain. The algorithm utilizes a tree-cotree decomposition to reduce the dimension of the eigenvalue problem. It is suitable for domains of general topology and is validated through numerical experiments.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
Lady Angelo, Jessika Camano, Sergio Caucao
Summary: In this paper, a new mixed variational formulation for a stationary magnetohydrodynamic flows in porous media problem is introduced and analyzed. The resulting mixed scheme is proven to be stable, convergent, and optimal a priori error estimates are obtained. Numerical tests are conducted to validate the theoretical results.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
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)