Article
Engineering, Multidisciplinary
Felipe V. Caro, Vincent Darrigrand, Julen Alvarez-Aramberri, Elisabete Alberdi, David Pardo
Summary: This work extends an automatic energy-norm hp-adaptive strategy to non-elliptic problems and goal-oriented adaptivity. It proposes an error indicator for quasi-optimal hp-unrefinements based on a multi-level hierarchical data structure and alternating h- and p-refinements. The strategy eliminates the basis functions with the lowest contributions to the solution, improving efficiency and accuracy.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Carsten Carstensen, Rui Ma
Summary: The collective marking strategy combined with alternative refinement indicators has been proven to achieve optimal convergence rates in adaptive mesh refining of LSFEMs. By utilizing explicit identities for the lowest-order Raviart-Thomas and Crouzeix-Raviart finite elements, this study extends the results to arbitrary polynomial degrees and mixed boundary conditions, with novel arguments. The analysis focuses on the Poisson equation in 3D with mixed boundary conditions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Petroleum
X. Raynaud, A. Pizzolato, A. Johansson, F. Caresani, A. Ferrari, O. Moyner, H. M. Nilsen, A. Cominelli, K-A Lie
Summary: This study aims to identify discretization errors caused by non-K-orthogonal grids upfront and compare representative, state-of-the-art consistent discretization methods, proposing error indicators and using tracer simulations to assess the impact of these errors. NTPFA and AvgMPFA were found to be the most viable solutions for integration into a commercial simulator, with the linear AvgMPFA method being the least invasive.
Article
Mathematics, Applied
Andreas Schafelner, Panayot S. Vassilevski
Summary: Researchers conducted a follow-up computational study on the recently proposed CFOSLS method, combined with parallel adaptive mesh refinement in four-dimensional space-time. Extensive computational experiments demonstrate the feasibility of the combined space-time AMR approach in both two and three spatial dimensions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Marcello Longo
Summary: This paper introduces novel adaptive methods for approximating the moments of solutions to partial differential equations (PDEs) with uncertain parametric inputs. These methods use deterministic quasi-Monte Carlo integration rules derived from Polynomial lattices, allowing for efficient numerical approximation of high-dimensional integrals without the curse of dimensionality.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Alex Bespalov, David J. Silvester, Feng Xu
Summary: A general adaptive refinement strategy is proposed in this paper for solving linear elliptic partial differential equations with random data. The strategy extends the a posteriori error estimation framework to cover problems with a nonaffine parametric coefficient dependence.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Interdisciplinary Applications
Carlos A. Moreira, Manuel A. Caicedo, Miguel Cervera, Michele Chiumenti, Joan Baiges
Summary: This work introduces a distributed memory machine and octree-based Finite Element framework for modeling metal Additive Manufacturing processes. The framework accurately captures the complex geometry and physical phenomena using Adaptive Mesh Refinement, while keeping the number of FEs controlled.
COMPUTATIONAL MECHANICS
(2023)
Article
Mathematics, Applied
Gregor Gantner, Dirk Praetorius
Summary: In this study, h-adaptive algorithms are considered in the context of the finite element method and the boundary element method. Under general assumptions on the building blocks SOLVE, ESTIMATE, MARK, and REFINE, it is proven that the adaptive algorithm converges to zero in terms of the underlying a posteriori error estimator. Unlike existing literature, this analysis does not rely on reliability and efficiency estimates but only on the structural properties of the estimator.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Francesco Dell'Accio, Filomena Di Tommaso, Allal Guessab, Federico Nudo
Summary: This study proposes a method of enriching the standard simplicial linear finite element by non-polynomial functions, and provides necessary and sufficient conditions for the existence of enriched element families. It is also shown that the enriched basis functions can be represented in a closed form using enrichment functions and functionals. Finally, numerical tests are conducted. This approach can address the under-performance of low-order elements in nearly incompressible materials.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
S. J. van den Boom, J. Zhang, F. van Keulen, A. M. Aragon
Summary: Smooth geometry description is crucial in design optimization, and combining level set description with a new enriched topology optimization methodology can generate correct topologies without the drawbacks of existing enriched methods.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Nuclear Science & Technology
Ni Dai, Bin Zhang, Xinyu Wang, Daogang Lu, Yixue Chen
Summary: This paper presents an hp-angular adaptivity algorithm for Boltzmann transport applications with strong angular effects. The algorithm updates both the angular mesh and the degree of the discontinuous finite element basis functions, allowing for different angular local refinement in space. Regular and goal-based error metrics are used to locate the regions to be refined. A mapping algorithm is developed to pass the angular solution between spatial regions with different quadrature sets. The results demonstrate the efficiency of this hp-angular adaptivity in resolving complex fluxes with relatively few angular unknowns.
NUCLEAR ENGINEERING AND TECHNOLOGY
(2023)
Article
Engineering, Civil
Manyu Xiao, Sougata Mukherjee, Balaji Raghavan, Subhrajit Dutta, Piotr Breitkopf, Weihong Zhang
Summary: This study investigates the effects of p-refinement in SIMP topology optimization, comparing optimized topologies, compliance values, and CPU clock time for various 2D classical benchmark problems.
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
Lexiang Yan, Rong An
Summary: In this paper, two-level finite element methods are proposed for the steady bio-convection flows problem. The MINI element is used to approximate the velocity and pressure, while the piecewise linear element is used to approximate the concentration. Error estimates of the finite element solutions are derived for the one-level method using the Aubin-Nitsche method. Two-level Stokes/Oseen/Newton finite element methods are proposed by combining two-level discretization technique, and optimal error estimates for the velocity and concentration in L1-norm and the pressure in L2-norm are obtained. Numerical results are provided to validate the theoretical analysis and assess the efficiency of the two-level methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Anna Ochal, Michal Jureczka, Piotr Bartman
Summary: This paper presents an abstract nonsmooth optimization problem and provides a numerical scheme to approximate its solution. Additionally, the theory is applied to solve a static contact problem and three computational methods for solving contact mechanical problems are compared.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Materials Science, Multidisciplinary
Sebastian Florez, Karen Alvarado, Marc Bernacki
Summary: The method introduced in this article is a new simulation approach for evolving multi-domains problems, which focuses on the effects of grain growth and grain boundary migration on stored energy due to dislocations. The methodology utilizes a front-tracking approach and further developments and studies were conducted on the model to better understand dynamic recrystallization phenomena.
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
(2021)
Article
Materials Science, Multidisciplinary
Sebastian Florez, Karen Alvarado, Brayan Murgas, Nathalie Bozzolo, Dominique Chatain, Carl E. Krill, Mingyan Wang, Gregory S. Rohrer, Marc Bernacki
Summary: Through 2D anisotropic full-field simulations, this article demonstrates how torque effects can complicate discussions regarding the kinetics of interface migration during grain growth. Neglecting torque effects in full-field formulations can significantly impact the overall rate of grain growth, the shape of grains and grain boundaries, as well as their local kinetics. The reduced mobility observed may be more complex than expected, without necessarily questioning the influence of curvature on the local kinetic equation.
Article
Materials Science, Multidisciplinary
Saoussen Ouhiba, Alexis Nicolay, Laurent Boissonnet, Marc Bernacki, Nathalie Bozzolo
Summary: This study investigates the potential factors contributing to the development of coarse recrystallized grains in 6xxx aluminum alloys during hot rolling. The results show that stored energy is the key factor behind grain overgrowth. The behavior and characteristics of coarse recrystallized grain boundaries are also examined.
METALLURGICAL AND MATERIALS TRANSACTIONS A-PHYSICAL METALLURGY AND MATERIALS SCIENCE
(2022)
Article
Chemistry, Physical
Brayan Murgas, Baptiste Flipon, Nathalie Bozzolo, Marc Bernacki
Summary: Two finite element level-set (FE-LS) formulations were compared for the modeling of grain growth of 316L stainless steel. The anisotropic formulation better predicted grain morphologies and respected the experimental data more accurately.
Article
Geochemistry & Geophysics
Andrew J. Ryan, Daniel Pino Munoz, Marc Bernacki, Marco Delbo, Naoya Sakatani, Jens Biele, Joshua P. Emery, Benjamin Rozitis
Summary: The thermal conductivity of granular planetary regolith is influenced by the porosity and particle packing density. Research shows that random packings of regolith have higher radiative thermal conductivity compared to ordered packings. A new empirical model has been developed to understand the relationship between regolith thermal conductivity, porosity, temperature, particle size, and the thermal conductivity of individual particles.
JOURNAL OF GEOPHYSICAL RESEARCH-PLANETS
(2022)
Article
Computer Science, Interdisciplinary Applications
Modesar Shakoor, Chung Hae Park
Summary: In this article, a multiscale approach is proposed for the computational homogenization of unsteady incompressible flows in domains containing small obstacles. The method, implemented using finite element analysis, shows robustness and efficiency in terms of computational cost and accuracy.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2023)
Article
Engineering, Multidisciplinary
Krushna Shinde, Vincent Itier, Jose Mennesson, Dmytro Vasiukov, Modesar Shakoor
Summary: This paper proposes an original approach based on an autoencoder neural network to construct a nonlinear Reduced-Order Model for a highly nonlinear brittle fracture problem. The effectiveness of the autoencoder in dimensionality reduction or compression of highly nonlinear data is demonstrated through a set of simulations. A complete deep learning framework is introduced to predict crack propagation patterns directly from the loading conditions. The proposed approach is validated using data sets generated for two problems with proportional and non-proportional loading conditions, evaluating its capabilities.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Materials Science, Multidisciplinary
N. Chandrappa, M. Bernacki
Summary: A novel finite element level-set based full-field numerical formulation is proposed to simulate diffusive solid-solid phase transformation in two-phase metallic alloys. The proposed method considers concomitant mechanisms such as recrystallization and grain growth, and its effectiveness is demonstrated in several test cases.
COMPUTATIONAL MATERIALS SCIENCE
(2023)
Article
Mechanics
Xiao Ma, Yang Chen, Modesar Shakoor, Dmytro Vasiukov, Stepan V. Lomov, Chung Hae Park
Summary: This paper focuses on the numerical implementation of phase-field models of fracture using the Fast Fourier Transform based numerical method. The influence of a simplification in the phase-field evolution equation on heterogeneous materials is assessed and a complete formulation is proposed. The assessment shows that the simplified formulation leads to artificial diffusion of damage between different components, while the complete formulation suppresses this diffusion.
ENGINEERING FRACTURE MECHANICS
(2023)
Article
Chemistry, Physical
Victor Grand, Baptiste Flipon, Alexis Gaillac, Marc Bernacki
Summary: This paper proposes a full-field numerical framework to predict the evolution of subgrain structures during hot forming. Two strategies are proposed to consider the subgrain structure, and the grain growth of a fully substructured microstructure is modeled. The results show that the selective growth of subgrains is affected by the mobility function. The recrystallization kinetics are quantitatively compared with different criteria, and the framework's ability to model continuous dynamic and post-dynamic recrystallization is assessed. The application of these numerical tools to other conditions and structures will be presented in a future article.
Article
Engineering, Manufacturing
E. Syerko, T. Schmidt, D. May, C. Binetruy, S. G. Advani, S. Lomov, L. Silva, S. Abaimov, N. Aissa, I. Akhatov, M. Ali, N. Asiaban, G. Broggi, J. Bruchon, B. Caglar, H. Digonnet, J. Dittmann, S. Drapier, A. Endruweit, A. Guilloux, R. Kandinskii, A. Leygue, B. Mahato, P. Martinez-Lera, M. Matveev, V. Michaud, P. Middendorf, N. Moulin, L. Orgeas, C. H. Park, S. Rief, M. Rouhi, I. Sergeichev, M. Shakoor, O. Shishkina, Y. Swolfs, M. Tahani, R. Umer, K. Vanclooster, R. Vorobyev
Summary: This paper presents the results of an international virtual permeability benchmark, which is a first contribution to permeability predictions for fibrous reinforcements based on real images. In this first stage, the focus was on the microscale computation of fiber bundle permeability. The scatter of the predicted axial permeability after the elimination of inconsistent results was found to be smaller (14%) than that of the transverse permeability (similar to 24%).
COMPOSITES PART A-APPLIED SCIENCE AND MANUFACTURING
(2023)
Article
Chemistry, Physical
Romain Agogue, Modesar Shakoor, Pierre Beauchene, Chung Hae Park
Summary: This study presents a numerical analysis of the effects of race tracking on the formation of dry spots and the accuracy of permeability measurement during the resin-transfer-molding process. Randomly generated defects are assessed using a Monte Carlo simulation method in the numerical simulation of the mold-filling process. The influence of race tracking on unsaturated permeability measurement and dry spot formation is investigated on flat plates. The results show that race-tracking defects near the injection gate can increase the measured unsaturated permeability by up to 40%.
Article
Mechanics
Xiao Ma, Dmytro Vasiukov, Modesar Shakoor, Stepan V. Lomov, Chung Hae Park
Summary: This paper focuses on the numerical implementation of phase-field models of fracture using the Fast Fourier Transform (FFT) based numerical method. The choice of regularization length in phase-field models is important for both macroscopic mechanical behavior and local crack propagation patterns. Wu's phase-field model has been successful in reducing length sensitivity for homogeneous materials, and it has also been found to be more suitable than Miehe's model for brittle failure with the introduction of an elastic stage. The sensitivity of Wu's model for heterogeneous materials has also been investigated in this study.
ENGINEERING FRACTURE MECHANICS
(2023)
Article
Materials Science, Multidisciplinary
Victor Grand, Baptiste Flipon, Alexis Gaillac, Marc Bernacki
Summary: A recently developed full-field level-set model of continuous dynamic recrystallization is applied to simulate zircaloy-4 recrystallization. The influence of strain rate, final strain, and initial microstructure is investigated, and the recrystallization heterogeneity is quantified. The simulation results replicate experimental observations and capture the recrystallization heterogeneity induced by different initial microstructures. Additionally, simulations with different numerical formulations demonstrate the role of intragranular dislocation density heterogeneities in the preferential growth of recrystallized grains.
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
(2023)
Article
Chemistry, Physical
Marion Roth, Baptiste Flipon, Nathalie Bozzolo, Marc Bernacki
Summary: This article compares different mean-field models under grain-growth conditions, with a focus on the consideration of topology in the neighborhood construction. Experimental data and material parameters are used for model comparisons. The study finds that topological models can improve predictions in monomodal cases, but show little difference compared to classical mean-field models in bimodal cases.