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1
Liu, Wing Kam, Su Hao, Ted Belytschko, Shaofan Li und Chin Tang Chang. „Multi-scale methods“. International Journal for Numerical Methods in Engineering 47, Nr. 7 (10.03.2000): 1343–61. http://dx.doi.org/10.1002/(sici)1097-0207(20000310)47:7<1343::aid-nme828>3.0.co;2-w.
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Podsiadlo, P., und G. W. Stachowiak. „Multi-scale representation of tribological surfaces“. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 216, Nr. 6 (01.06.2002): 463–79. http://dx.doi.org/10.1243/135065002762355361.
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Many numerical surface topography analysis methods exist today. However, even for the moderately complicated topography of a tribological surface these methods can provide only limited information. The reason is that tribological surfaces often exhibit a non-stationary and multi-scale nature while the numerical methods currently used work well with surface data exhibiting a stationary random process and provide surface descriptors closely related to a scale at which surface data were acquired. The suitability of different methods, including Fourier transform, windowed Fourier transform, Cohen's class distributions (especially the Wigner-Ville distribution), wavelet transform, fractal methods and a hybrid fractal-wavelet method, for the analysis of tribological surface topographies is investigated in this paper. The method best suited to this purpose has been selected.
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Liu, Miao, Yan Cao, Zhijie Wang und Chaorui Nie. „Multi-scale Numerical Simulation of Powder Metallurgy Densification Process“. Journal of Physics: Conference Series 2501, Nr. 1 (01.05.2023): 012022. http://dx.doi.org/10.1088/1742-6596/2501/1/012022.
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Abstract In order to reduce defects such as pores, gold phases and cracks in powder metallurgy, scholars have studied the densification process of powder metallurgy. Based on the study of the powder metallurgy deformation mechanism, this paper classifies and summarizes the numerical simulation theory and the methods. At present, the numerical simulation of the densification process of powder metallurgy is carried out mainly in macroscopic, mesoscopic and microscopic directions. Macro scale is an application of finite element method based on continuum theory. The meso-scale is an application of the discrete element method based on the discontinuous media theory. Cellular automata simulation is the main numerical simulation method in the microscale. Different modeling theories and methods have their own adaptability and limitations. By combining the numerical simulation theory and the method of various scales, the process of densification of the material can be realized more accurately and accurately.
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Chen, Li, Ya-Ling He, Qinjun Kang und Wen-Quan Tao. „Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes“. Journal of Computational Physics 255 (Dezember 2013): 83–105. http://dx.doi.org/10.1016/j.jcp.2013.07.034.
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Engquist, B., und P. E. Souganidis. „Asymptotic and numerical homogenization“. Acta Numerica 17 (25.04.2008): 147–90. http://dx.doi.org/10.1017/s0962492906360011.
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Homogenization is an important mathematical framework for developing effective models of differential equations with oscillations. We include in the presentation techniques for deriving effective equations, a brief discussion on analysis of related limit processes and numerical methods that are based on homogenization principles. We concentrate on first- and second-order partial differential equations and present results concerning both periodic and random media for linear as well as nonlinear problems. In the numerical sections, we comment on computations of multi-scale problems in general and then focus on projection-based numerical homogenization and the heterogeneous multi-scale method.
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Krause, Rolf, und Christina Mohr. „Level set based multi-scale methods for large deformation contact problems“. Applied Numerical Mathematics 61, Nr. 4 (April 2011): 428–42. http://dx.doi.org/10.1016/j.apnum.2010.11.007.
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Gai, Wen Hai, R. Guo und Jun Guo. „Molecular Dynamics Approach and its Application in the Analysis of Multi-Scale“. Applied Mechanics and Materials 444-445 (Oktober 2013): 1364–69. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.1364.
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Numerical simulation of the behavior of materials can be used as a versatile, efficient and low cost tool for developing an understanding of material behavior [. The numerical simulation methods include quantum mechanics, molecular dynamics, Voronoi cell finite element method and finite element method et al. These methods themselves are not sufficient for many fundamental problems in computational mechanics, and the deficiencies lead to the thrust of multiple-scale methods. The multi-scale method to model micro-scale systems by coupled continuum mechanics and molecular dynamics was introduced. This paper describes the basic methods of multi-scale and general simulation process of molecular dynamics was reviewed.
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Tremmel, Stephan, Max Marian, Benedict Rothammer, Tim Weikert und Sandro Wartzack. „Designing Amorphous Carbon Coatings Using Numerical and Experimental Methods within a Multi-Scale Approach“. Defect and Diffusion Forum 404 (Oktober 2020): 77–84. http://dx.doi.org/10.4028/www.scientific.net/ddf.404.77.
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Amorphous carbon coatings have the potential to effectively reduce friction and wear in tribotechnical systems. The appropriate application of amorphous carbon layers requires both, a very good understanding of the tribological system and knowledge of the relationships between the fabrication of the coatings and their properties. In technical practice, however, the coatings’ development and their selection on the one hand and the design of the tribological system and its environment on the other hand are usually very strongly separated. The present work therefore aims to motivate the integrated development of tribotechnical systems with early consideration of the potential of amorphous carbon coatings. An efficient integrated development process is presented, which makes it possible to determine the boundary conditions and the load collective of the tribological system based upon an overall system and to derive the requirements for a tailored coating. In line with the nature of tribology, this approach must cover several scales. In this respect, the development process follows a V-model. The left branch of the V-model is mainly based upon a simulation chain including multibody and contact simulations. The right branch defines an experimental test chain comprising coating characterization to refine the contact simulation iteratively and tribological testing on different levels to validate the function fulfillment. Within this contribution, the outlined approach is illustrated by two use cases, namely the cam/tappet-pairing and the total knee replacement.
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Schmidt, Alexander A., Yuri V. Trushin, K. L. Safonov, V. S. Kharlamov, Dmitri V. Kulikov, Oliver Ambacher und Jörg Pezoldt. „Multi-Scale Simulation of MBE-Grown SiC/Si Nanostructures“. Materials Science Forum 527-529 (Oktober 2006): 315–18. http://dx.doi.org/10.4028/www.scientific.net/msf.527-529.315.
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The main obstacle for the implementation of numerical simulation for the prediction of the epitaxial growth is the variety of physical processes with considerable differences in time and spatial scales taking place during epitaxy: deposition of atoms, surface and bulk diffusion, nucleation of two-dimensional and three-dimensional clusters, etc. Thus, it is not possible to describe all of them in the framework of a single physical model. In this work there was developed a multi-scale simulation method for molecular beam epitaxy (MBE) of silicon carbide nanostructures on silicon. Three numerical methods were used in a complex: Molecular Dynamics (MD), kinetic Monte Carlo (KMC), and the Rate Equations (RE). MD was used for the estimation of kinetic parameters of atoms at the surface, which are input parameters for other simulation methods. The KMC allowed the atomic-scale simulation of the cluster formation, which is the initial stage of the SiC growth, while the RE method gave the ability to study the growth process on a longer time scale. As a result, a full-scale description of the surface evolution during SiC formation on Si substrates was developed.
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Altmann, Robert, Patrick Henning und Daniel Peterseim. „Numerical homogenization beyond scale separation“. Acta Numerica 30 (Mai 2021): 1–86. http://dx.doi.org/10.1017/s0962492921000015.
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Numerical homogenization is a methodology for the computational solution of multiscale partial differential equations. It aims at reducing complex large-scale problems to simplified numerical models valid on some target scale of interest, thereby accounting for the impact of features on smaller scales that are otherwise not resolved. While constructive approaches in the mathematical theory of homogenization are restricted to problems with a clear scale separation, modern numerical homogenization methods can accurately handle problems with a continuum of scales. This paper reviews such approaches embedded in a historical context and provides a unified variational framework for their design and numerical analysis. Apart from prototypical elliptic model problems, the class of partial differential equations covered here includes wave scattering in heterogeneous media and serves as a template for more general multi-physics problems.
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Perera, M. S. M., S. Theodossiades und H. Rahnejat. „A multi-physics multi-scale approach in engine design analysis“. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 221, Nr. 3 (01.09.2007): 335–48. http://dx.doi.org/10.1243/14644193jmbd78.
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Vibration behaviour of an internal combustion engine depends on rigid body inertial dynamics, structural modal characteristics of its elastic members, tribological behaviour of loadbearing contacts, and piston-cylinder interactions. Therefore, it is essential to use a multi-physics approach that addresses all these physical properties in a single integrative model as presented in this paper. This approach can be regarded as holistic and a good aid for detailed design. Particular attention is paid to the critical elements in the system, such as load-bearing conjunctions (crankshaft main bearings) and piston-cylinder wall interactions. Another important feature is the integrated analysis across the physics of motion from microscale fluid film formation to submillimetre structural deformations and onto large displacements of inertial members. In order to succeed in predictions within sensible industrial time scales, analytical methods have been used as far as possible rather than numerical approaches. Model predictions show good agreement with fired engine test data.
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Zhang, Jie, Fan Shun Meng und Yang Sen Li. „The Study of the Difference Methods with Variable Grids Seismic Wave Numerical Simulation in Multi-Scale Complex Media“. Advanced Materials Research 1055 (November 2014): 254–58. http://dx.doi.org/10.4028/www.scientific.net/amr.1055.254.
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In the process of seismic wave field numerical simulation using finite difference method, the simulation accuracy and computational efficiency is one of the keys to the problem which is especially important to the numerical simulation of small scale geological body which velocity changes violently. In order to describe the local structure of medium subtly and guarantee the efficiency of the simulation, this article introduces the variable grid finite difference method to the staggered grid high-order finite difference numerical simulation on the basic of the traditional staggered grid finite difference algorithm to improve the staggered grid spatial algorithm and avoid the reduction of the simulation accuracy and computational efficiency caused by the interpolation factor. The results show that the variable staggered grid numerical simulation of finite difference algorithm can accurately depict the space variation of underground medium physical properties to further enhance the adaptability of numerical simulation of complex medium, it also can provide reliable basis for wave field imaging and the combined interpretation of p-wave and s-wave.
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Roeber, Volker, J. Dylan Nestler, Jonas Pinault, Assaf Azouri und Florian Bellafont. „MULTI-SCALE INFRA-GRAVITY WAVE DYNAMICS - THE FRENCH BASQUE COAST“. Coastal Engineering Proceedings, Nr. 36v (28.12.2020): 46. http://dx.doi.org/10.9753/icce.v36v.waves.46.
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Phase-resolving numerical models are a powerful tool to identify and analyze dominant wave processes along a site of interest. We have carried out a numerical study related to infra-gravity wave dynamics along the French Basque coast. The computed scenarios are representative for the swell conditions at the site of interest and include variations in offshore wave height, direction, and water level. Several statistical methods were employed that illustrate that the irregular bathymetry is a key component for the strong variations in sea-swell and IG-wave energy. The water level is demonstrated to substantially affect the IG-wave behavior, more than the wave direction. Swash oscillations in the IG-frequency band are greater than or equal to sea-swell swash oscillations at nearly all locations along the studied shoreline.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/ELZwJCokkX0
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Zhao, Xiaoyi, Zhile Shu und Xiangjun Pei. „Research and Perspectives on Fire-Fighting Systems in Tunnels under Strong Piston Wind Action“. Buildings 13, Nr. 2 (04.02.2023): 435. http://dx.doi.org/10.3390/buildings13020435.
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Guided by the technical requirements for tunnel fire safety, an overview of tunnel piston wind, combustion models, and full-size and small tunnel fire tests is presented. Firstly, the theoretical model and numerical calculation methods for piston wind tunnel fires are presented from the perspective of numerical simulation. Then, full-scale and small-scale test models for tunnel fires are presented, and the advantages and disadvantages of single-row, multi-row, single-fire source, and multi-fire source test methods are described. Finally, key breakthrough directions for future numerical and experimental research on piston winds and tunnel fires are proposed, specifically the mastery of underground tunnel fire development prediction methods. This involves mastering the full-scene elemental fire testing technology for underground tunnel operation systems; developing multi-channel data acquisition technology for fire tests under the effect of multiple disturbances such as high temperature and high humidity; and mastering the smoke flow law during fires in complex tunnel projects.
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Zhao, Hai Tao, Dong Hui Huang, Pan Xiu Wang, Qiao Li und Qing Ning. „Research Advances on Multi-Scale Modeling of Properties of Cement-Based Materials“. Applied Mechanics and Materials 195-196 (August 2012): 291–96. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.291.
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Cement-based material is a complex multi-scale material which is difficult to comprehend. With the simulation model, the methods and examples of multi-scale modeling of structure and performance of cement-based materials are presented based on coupled cementitious composites and structural mechanics. This paper discuss on the properties of cement-based materials as shrinkage, elasticity, durability which are carried out by numerical methods such as Finite Element Method (FEM) and eXtended FEM(XFEM).
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Zhang, Li Qiang, Ping Yang, Fang Wei Xie, Tao Xi, Xin Gang Yu und Xi Fu Song. „MD-ISE-FE Multiscale Modeling and Numerical Simulation of Thermal Conductivity of Cu Film Interface Structure“. Advanced Materials Research 382 (November 2011): 242–46. http://dx.doi.org/10.4028/www.scientific.net/amr.382.242.
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With the devices miniaturization, the properties of materials at the micro/nano scale were much different from what at Macro-scale because of the scale effect. The Interface Stress Element (ISE) was introduced into the multi-scale model. These three methods, Molecular Dynamics (MD), ISE and Finite Element (FE) were effectively combined by designing a handshake region and using the transition interface element method. The multi-scale model of film was built based on MD-ISE-FE. The sequential coupling method was used to calculate, and then, the results of the FE and ISE region were applied to the MD region. The EAM potential was used to simulate. The results were the basically same with the other experimental and simulation results in the reference. It indicated that the multi-scale analysis method could be applied to calculate the thermodynamics properties of the interface structure at the Micro/nano scale.
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Yang, Dong, Wei Xin Ren und Xiang Xiao. „Structure Dynamic Signal Denoise Using Multi-Scale EMD“. Advanced Materials Research 168-170 (Dezember 2010): 2611–14. http://dx.doi.org/10.4028/www.scientific.net/amr.168-170.2611.
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For structure dynamic signals with low signal to noise ratio (SNR), Multi-scale EMD is proposed to extract useful information from signals contaminated by noise. This method is an adaptive way, and achieves better performance than traditional methods. A complex signal composed of signal and noise, which is first decompose into a series of different characteristic IMFs. Then sum of the first few IMFs including useful information and noise are further decomposed by EMD, and iterate this process for several times in order to extract useful information. The final step is deleting some IMFs obtained from the last decomposing which is considered as noise, and rebuilt the signal using the rest IMFs from different scale. This method can smooth signal effectively. The effectiveness of the proposed method is verified with the numerical simulating signal, and useful information in signals is retained. It also has some superior performances such as concise computer process, robust application, etc.
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Castro, C. E., M. Käser und E. F. Toro. „Space–time adaptive numerical methods for geophysical applications“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, Nr. 1907 (28.11.2009): 4613–31. http://dx.doi.org/10.1098/rsta.2009.0158.
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In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space–time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost.
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Behrens, J., und F. Dias. „New computational methods in tsunami science“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, Nr. 2053 (28.10.2015): 20140382. http://dx.doi.org/10.1098/rsta.2014.0382.
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Tsunamis are rare events with severe consequences. This generates a high demand on accurate simulation results for planning and risk assessment purposes because of the low availability of actual data from historic events. On the other hand, validation of simulation tools becomes very difficult with such a low amount of real-world data. Tsunami phenomena involve a large span of spatial and temporal scales—from ocean basin scales of to local coastal wave interactions of or even , or from resonating wave phenomena with durations of to rupture with time periods of . The scale gap of five orders of magnitude in each dimension makes accurate modelling very demanding, with a number of approaches being taken to work around the impossibility of direct numerical simulations. Along with the mentioned multi-scale characteristic, the tsunami wave has a multitude of different phases, corresponding to different wave regimes and associated equation sets. While in the deep ocean, wave propagation can be approximated relatively accurately by linear shallow-water theory, the transition to a bore or solitary wave train in shelf areas and then into a breaking wave in coastal regions demands appropriate mathematical and numerical treatments. The short duration and unpredictability of tsunami events pose another challenging requirement to tsunami simulation approaches. An accurate forecast is sought within seconds with very limited data available. Thus, efficiency in numerical solution processes and at the same time the consideration of uncertainty play a big role in tsunami modelling applied for forecasting purposes.
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Marín, F., F. Alhama, J. Solano, P. A. Meroño und J. F. Sánchez. „Multi-scale Simulations of Dry Friction Using Network Simulation Method“. Applied Mathematics and Nonlinear Sciences 1, Nr. 2 (23.11.2016): 559–80. http://dx.doi.org/10.21042/amns.2016.2.00044.
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AbstractThe study of everyday phenomena involving friction continues to maintain a high level of difficulty despite its long history. The causes of this problem lie in the different scale of the characteristics of the phenomenon, macroscopic and microscopic. Thus, very different models, valid in a narrow scope which prevents generalization, have been appearing. This survey presents the application of network simulation method to the numerical solution to the study of friction at very different scales. On the one hand, on a microscopic scale an atomic force microscope model has been studied, related to the analysis of soft surfaces at the atomic scale. Furthermore, on a macroscopic scale model related to the analysis of an industrial device, such as a brake mechanism has been studied. After presenting herein is a review of the different formulations of the friction force, the nature of the surfaces involved in the phenomenon, as well as the definition of the problems to be analyzed. The design of network models and the implementation of the initial conditions are explained. The results of the application of network models to selected problems are presented. In order to verify the reliability of the proposed models, their results are compared with the solutions obtained by other numerical methods or experimental results, one from a device developed during the preparation of this report.
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Porion, Patrice, Ali Asaad, Thomas Dabat, Baptiste Dazas, Alfred Delville, Eric Ferrage, Fabien Hubert et al. „Water and Ion Dynamics in Confined Media: A Multi-Scale Study of the Clay/Water Interface“. Colloids and Interfaces 5, Nr. 2 (15.06.2021): 34. http://dx.doi.org/10.3390/colloids5020034.
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This review details a large panel of experimental studies (Inelastic Neutron Scattering, Quasi-Elastic Neutron Scattering, Nuclear Magnetic Resonance relaxometry, Pulsed-Gradient Spin-Echo attenuation, Nuclear Magnetic Resonance Imaging, macroscopic diffusion experiments) used recently to probe, over a large distribution of characteristic times (from pico-second up to days), the dynamical properties of water molecules and neutralizing cations diffusing within clay/water interfacial media. The purpose of this review is not to describe these various experimental methods in detail but, rather, to investigate the specific dynamical information obtained by each of them concerning these clay/water interfacial media. In addition, this review also illustrates the various numerical methods (quantum Density Functional Theory, classical Molecular Dynamics, Brownian Dynamics, macroscopic differential equations) used to interpret these various experimental data by analyzing the corresponding multi-scale dynamical processes. The purpose of this multi-scale study is to perform a bottom-up analysis of the dynamical properties of confined ions and water molecules, by using complementary experimental and numerical studies covering a broad range of diffusion times (between pico-seconds up to days) and corresponding diffusion lengths (between Angstroms and centimeters). In the context of such a bottom-up approach, the numerical modeling of the dynamical properties of the diffusing probes is based on experimental or numerical investigations performed on a smaller scale, thus avoiding the use of empirical or fitted parameters.
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Yin, Xiangjie, Hang Lin, Yifan Chen, Yixian Wang und Yanlin Zhao. „Precise evaluation method for the stability analysis of multi-scale slopes“. SIMULATION 96, Nr. 10 (03.08.2020): 841–48. http://dx.doi.org/10.1177/0037549720943274.
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Slope stability analysis is a multi-scale problem. Typically, owing to the distinctions of slope scales (e.g., slope height or slope angle) in practical engineering, the stability calculation results of slopes with various scales from numerical methods inevitably exhibit different computational precision levels in the case of identical computational grids, and therefore the stability results of different slopes cannot be compared. To achieve equal accuracy stability analysis for multi-scale slopes, this study establishes numerical models of slopes with various scales as well as different grid shapes and sizes to conduct stability analysis. The results show the following: (a) a positive correlation relationship exists between the safety factor of the slope and the scaling factor, which is defined as the ratio of the grid size to the slope height; (b) the definition of the refined safety factor is given, representing the safety factor that corresponds to the infinitesimal grid size and eliminating the computational error of slope stability analysis caused by grid size or shape; (c) on this basis, embarking on the composite influence of multiple scales of slope on stability analysis, the study proposes a simplified treatment method suitable for evaluating the refined safety factor of the multi-scale slopes, which is verified as valid and feasible by some examples.
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Bernabeu, Miguel O., Rafel Bordas, Pras Pathmanathan, Joe Pitt-Francis, Jonathan Cooper, Alan Garny, David J. Gavaghan, Blanca Rodriguez, James A. Southern und Jonathan P. Whiteley. „C haste : incorporating a novel multi-scale spatial and temporal algorithm into a large-scale open source library“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, Nr. 1895 (28.05.2009): 1907–30. http://dx.doi.org/10.1098/rsta.2008.0309.
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Recent work has described the software engineering and computational infrastructure that has been set up as part of the Cancer, Heart and Soft Tissue Environment (C haste ) project. C haste is an open source software package that currently has heart and cancer modelling functionality. This software has been written using a programming paradigm imported from the commercial sector and has resulted in a code that has been subject to a far more rigorous testing procedure than that is usual in this field. In this paper, we explain how new functionality may be incorporated into C haste . Whiteley has developed a numerical algorithm for solving the bidomain equations that uses the multi-scale (MS) nature of the physiology modelled to enhance computational efficiency. Using a simple geometry in two dimensions and a purpose-built code, this algorithm was reported to give an increase in computational efficiency of more than two orders of magnitude. In this paper, we begin by reviewing numerical methods currently in use for solving the bidomain equations, explaining how these methods may be developed to use the MS algorithm discussed above. We then demonstrate the use of this algorithm within the C haste framework for solving the monodomain and bidomain equations in a three-dimensional realistic heart geometry. Finally, we discuss how C haste may be developed to include new physiological functionality—such as modelling a beating heart and fluid flow in the heart—and how new algorithms aimed at increasing the efficiency of the code may be incorporated.
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Trahan, Corey Jason, Mark Loveland, Noah Davis und Elizabeth Ellison. „A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods“. Entropy 25, Nr. 4 (28.03.2023): 580. http://dx.doi.org/10.3390/e25040580.
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Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.
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Grebennikov, Dmitry S. „Computational methods for multiscale modelling of virus infection dynamics“. Russian Journal of Numerical Analysis and Mathematical Modelling 38, Nr. 2 (01.03.2023): 75–87. http://dx.doi.org/10.1515/rnam-2023-0007.
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Abstract Virus infection dynamics is governed by the processes on multiple scales: on the whole organism level, tissue level, and intracellular level. In this paper, we develop a multi-scale multi-compartment model of HIV infection in a simplified setting and the computational methods for numerical realization of the model. The multiscale model describes the processes from various scales and of different nature (cell motility, virus diffusion, intracellular virus replication). Intracellular replication model is based on a Markov chain with time-inhomogeneous propensities that depend on the extracellular level of virions. Reaction diffusion equations used to model free virion diffusion in the lymphoid tissue have moving sources, which are determined by the positions of the infected cells (immune cell motility model) and the rate of virion secretion from them (intracellular model). Immune cell motility model parameterizes the intercellular interaction forces, friction and the stochastic force of active cell motility. Together, this allows for a proper description of the intracellular stochasticity that propagates across multiple scales. A hybrid discrete-continuous stochastic-deterministic algorithm for simulation of the multiscale model based on the uniformization Monte Carlo method is implemented.
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Wu, Yuching, und Jianzhuang Xiao. „Implementation of the Multiscale Stochastic Finite Element Method on Elliptic PDE Problems“. International Journal of Computational Methods 14, Nr. 01 (11.01.2017): 1750003. http://dx.doi.org/10.1142/s0219876217500037.
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In this study, a multi-scale finite element method was proposed to solve two linear scale-coupling stochastic elliptic PDE problems, a tightly stretched wire and flow through porous media. At microscopic level, the main idea was to form coarse-scale equations with a prescribed analytic form that may differ from the underlying fine-scale equations. The relevant stochastic homogenization theory was proposed to model the effective global material coefficient matrix. At the macroscopic level, the Karhunen–Loeve decomposition was coupled with a Polynomial Chaos expansion in conjunction with a Galerkin projection to achieve an efficient implementation of the randomness into the solution procedure. Various stochastic methods were used to plug the microscopic cell to the global system. Strategy and relevant algorithms were developed to boost computational efficiency and to break the curse of dimension. The results of numerical examples were shown consistent with ones from literature. It indicates that the proposed numerical method can act as a paradigm for general stochastic partial differential equations involving multi-scale stochastic data. After some modification, the proposed numerical method could be extended to diverse scientific disciplines such as geophysics, material science, biological systems, chemical physics, oceanography, and astrophysics, etc.
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Mukhametzyanov, Irik Z. „Transformation of numerical scales for pairwise comparisons: AHP, Dematel, BWM, SWARA“. Journal Of Applied Informatics 17, Nr. 5 (21.10.2022): 15–33. http://dx.doi.org/10.37791/2687-0649-2022-17-5-15-33.
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The paper presents an overview and comparative analysis of four weighting methods for multi-criteria decision-making problem based on pairwise comparisons: AHP, Dematel, BWM and SWARA. It is demonstrate, by examples that the reliability of evaluations largely depends on the correct use of the pairwise comparison tool: evaluations are given on a verbal scale, then converted into quantitative values and then the criteria priorities are calculated. All stages of pairwise comparisons are multivariate. In particular, the validity of this decision-making tool depends on the choice of numerical scale and the method of prioritization. Given the importance, a set of concepts relating to linguistic variables, linguistic pairwise comparison matrices, and numerical scale (scale function) are presented in detail. It is demonstrate that the information of the pairwise comparison matrix in AHP is higher and is sufficient for the unambiguous implementation of the Dematel, BWM and SWARA methods. Although the reliability of the solution for a larger number of input information is considered higher, nevertheless, it cannot be argued that the decision of the AHP are more significant. The emphasis in this study is on the transformation of the numerical scale. The transformation of the numerical scale a directly related to the mental representation of the verbal scale, since the decision maker forms the scale according to his mental representation. It is demonstrate that the compression of the numerical scale leads to the alignment of priorities. The trend is the same for all types of numerical scales and prioritization methods, but the process occurs at different speeds. For scales with a smaller number of gradations, a decrease in the degree of priority on the numerical scale is characteristic, which leads to a decrease in the difference in weights. In particular, this difference can be adjusted by scaling.
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Bhattacharyya, Mainak, David Dureisseix und Beatrice Faverjon. „Numerical homogenisation based on asymptotic theory and model reduction for coupled elastic-viscoplastic damage“. International Journal of Damage Mechanics 29, Nr. 9 (11.06.2020): 1416–44. http://dx.doi.org/10.1177/1056789520930785.
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This article deals with damage computation of heterogeneous structures containing locally periodic micro-structures. Such heterogeneous structure is extremely expensive to simulate using classical finite element methods, as the level of discretisation required to capture the micro-structural effects is too fine. The simulation time becomes even higher when dealing with highly non-linear material behaviour, e.g. damage, plasticity and such others. Therefore, a multi-scale strategy is proposed here that facilitates the simulation of non-linear heterogeneous material behaviour in a manner that is computationally feasible. Based on the asymptotic homogenisation theory, this multi-scale technique explores the micro–macro behaviour for elasto-(visco)plasticity coupled with damage. The theory inherently segregates the heterogeneous continua into a macroscopic homogeneous structure and an underlying heterogeneous microscopic periodic unit cell. Several heterogeneous structures have been simulated using the multi-scale method along with a one-dimensional verification with respect to a reference solution. Additionally, a reduced order modelling is used to prevent large memory requirement for storing micro-structural quantities of interest.
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Ruparel, Tejas, Azim Eskandarian und James D. Lee. „Concurrent Multi-Domain Simulations in Structural Dynamics Using Multiple Grid and Multiple Time-Scale (MGMT) Method“. International Journal of Computational Methods 15, Nr. 04 (24.05.2018): 1850021. http://dx.doi.org/10.1142/s0219876218500214.
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This paper describes a generic algorithm for concurrently solving multiple sub-domains that are selectively discretized in space and time. The mathematical background for this approach is largely based upon the fundamental principles of domain decomposition methods (DDM) and Lagrange multipliers. A proof of stability is provided using energy method and overall efficiency, accuracy and stability of multiple sub-domain coupling is evaluated using a series of numerical examples. Numerical stability is verified by ensuring energy balance at global as well as component sub-domain level. Discussed examples highlight the greatest advantage of MGMT method; which is high simulation speedups (at the cost of reasonably small errors).
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Comişel, H., Y. Narita und U. Motschmann. „Isotropy restoration toward high-beta space plasmas“. Nonlinear Processes in Geophysics Discussions 1, Nr. 2 (12.08.2014): 1313–30. http://dx.doi.org/10.5194/npgd-1-1313-2014.
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Abstract. Wavevector anisotropy of ion-scale plasma turbulence is studied at various values of beta. Two complementary methods are used. One is multi-point measurements of magnetic field in the near-Earth solar wind as provided by the Cluster spacecraft mission, and the other is hybrid numerical simulation of two-dimensional plasma turbulence. The both methods provide evidence of wavevector anisotropy as a function of beta such that isotropy is gradually restored toward higher values of beta. Furthermore, the numerical simulation study demonstrates the existence of scaling law between plasma beta and wavevector anisotropy. This fact can be used to construct a diagnostic tool to determine or to constrain plasma beta using multi-point magnetic field measurements in space.
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Chen, Xiaoxu, Tengyuan Wang, Chang Cai, Jianshuang Liu, Xiaoxia Gao, Naizhi Guo und Qingan Li. „A Review of Experiment Methods, Simulation Approaches and Wake Characteristics of Floating Offshore Wind Turbines“. Journal of Marine Science and Engineering 13, Nr. 2 (22.01.2025): 208. https://doi.org/10.3390/jmse13020208.
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With the urgent demand for net-zero emissions, renewable energy is taking the lead and wind power is becoming increasingly important. Among the most promising sources, offshore wind energy located in deep water has gained significant attention. This review focuses on the experimental methods, simulation approaches, and wake characteristics of floating offshore wind turbines (FOWTs). The hydrodynamics and aerodynamics of FOWTs are not isolated and they interact with each other. Under the environmental load and mooring force, the floating platform has six degrees of freedom motions, which bring the changes in the relative wind speed to the turbine rotor, and furthermore, to the turbine aerodynamics. Then, the platform’s movements lead to a complex FOWT wake evolution, including wake recovery acceleration, velocity deficit fluctuations, wake deformation and wake meandering. In scale FOWT tests, it is challenging to simultaneously satisfy Reynolds number and Froude number similarity, resulting in gaps between scale model experiments and field measurements. Recently, progress has been made in scale model experiments; furthermore, a “Hardware in the loop” technique has been developed as an effective solution to the above contradiction. In numerical simulations, the coupling of hydrodynamics and aerodynamics is the concern and a typical numerical simulation of multi-body and multi-physical coupling is reviewed in this paper. Furthermore, recent advancements have been made in the analysis of wake characteristics, such as the application of instability theory and modal decomposition techniques in the study of FOWT wake evolution. These studies have revealed the formation of vortex rings and leapfrogging behavior in adjacent helical vortices, which deepens the understanding of the FOWT wake. Overall, this paper provides a comprehensive review of recent research on FOWT wake dynamics.
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Soper, David, Dominic Flynn, Chris Baker, Adam Jackson und Hassan Hemida. „A comparative study of methods to simulate aerodynamic flow beneath a high-speed train“. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232, Nr. 5 (05.10.2017): 1464–82. http://dx.doi.org/10.1177/0954409717734090.
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The introduction of dedicated high-speed railway lines around the world has led to issues associated with running trains at very high speeds. Aerodynamic effects proportionally increase with train speed squared; consequently, at higher speeds aerodynamic effects will be significantly greater than those of trains travelling at lower speeds. On ballasted track beds, the phenomenon in which ballast particles become airborne during the passage of a high-speed train has led to the need for understanding the processes involved in train and track interaction (both aerodynamical and geotechnical). The difficulty in making full-scale aerodynamic measurements beneath a high-speed train has created the requirement to be able to accurately simulate these complex aerodynamic flows at the model scale. In this study, the results of moving-model tests and numerical simulations were analysed to determine the performance of each method for simulating the aerodynamic flow underneath a high-speed train. Validation was provided for both cases by juxtaposing the results against those from full-scale measurements. The moving-model tests and numerical simulations were performed at the 1/25th scale. Horizontal velocities from the moving-model tests and computational fluid dynamics simulations were mostly comparable except those obtained close to the ballast. In this region, multi-hole aerodynamic probes were unable to accurately measure velocities. The numerical simulations were able to resolve the flow to much smaller turbulent scales than could be measured in the experiments and showed an overshoot in peak velocity magnitudes. Pressure and velocity magnitudes were found to be greater in the numerical simulations than in the experimental tests. This is thought to be due to the influence of ballast stones in the experimental studies allowing the flow to diffuse through them, whereas in the computational fluid dynamics simulations, the flow stagnated on a smooth non-porous surface. Additional validation of standard deviations and turbulence intensities found good agreement between the experimental data but an overshoot in the numerical simulations. Both moving model and computational fluid dynamics techniques were shown to be able to replicate the flow development beneath a high-speed train. These techniques could therefore be used as a method to model underbody flow with a view to train homologation.
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Dong, Jieshi, Jinming He, Song Liu, Neng Wan und Zhiyong Chang. „A Multi-Scale Tool Orientation Generation Method for Freeform Surface Machining with Bull-Nose Tool“. Micromachines 14, Nr. 6 (05.06.2023): 1199. http://dx.doi.org/10.3390/mi14061199.
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Free-form surface parts are widely used in industries, and they consist of intricate 3D surfaces such as molds, impellers, and turbine blades that possess complex geometrical contours and demand high precision. Proper tool orientation is crucial for ensuring the efficiency and accuracy of five-axis computer numerical control (CNC) machining. Multi-scale methods have received much attention and have been widely used in various fields. They have been proven to be instrumental and can obtain fruitful outcomes. Ongoing research on multi-scale tool orientation generation methods, which aim to acquire tool orientations that satisfy both macro- and micro-scale requirements, is significantly important for improving the machining quality of workpiece surfaces. This paper proposes a multi-scale tool orientation generation method that considers both the machining strip width and roughness scales. This method also ensures a smooth tool orientation and avoids interference in the machining process. First, the correlation between the tool orientation and rotational axis is analyzed, and feasible area calculation and tool orientation adjustment methods are introduced. Then, the paper introduces the calculation method for machining strip widths on the macro-scale and the roughness calculation method on the micro-scale. Besides, tool orientation adjustment methods for both scales are proposed. Next, a multi-scale tool orientation generation method is developed to generate tool orientations that meet the macro- and micro-scale requirements. Finally, to verify the effectiveness of the proposed multi-scale tool orientation generation method, it is applied to the machining of a free-form surface. Experimental verification results have shown that the tool orientation generated by the proposed method can obtain the expected machining strip width and roughness, meeting both macro- and micro-scale requirements. Therefore, this method has significant potential for engineering applications.
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Folkard, Andrew. „The Multi-Scale Layering-Structure of Thermal Microscale Profiles“. Water 13, Nr. 21 (01.11.2021): 3042. http://dx.doi.org/10.3390/w13213042.
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Thermal microstructure profiling is an established technique for investigating turbulent mixing and stratification in lakes and oceans. However, it provides only quasi-instantaneous, 1-D snapshots. Other approaches to measuring these phenomena exist, but each has logistic and/or quality weaknesses. Hence, turbulent mixing and stratification processes remain greatly under-sampled. This paper contributes to addressing this problem by presenting a novel analysis of thermal microstructure profiles, focusing on their multi-scale stratification structure. Profiles taken in two small lakes using a Self-Contained Automated Micro-Profiler (SCAMP) were analysed. For each profile, buoyancy frequency (N), Thorpe scales (LT), and the coefficient of vertical turbulent diffusivity (KZ) were determined. To characterize the multi-scale stratification, profiles of d2T/dz2 at a spectrum of scales were calculated and the number of turning points in them counted. Plotting these counts against the scale gave pseudo-spectra, which were characterized by the index D of their power law regression lines. Scale-dependent correlations of D with N, LT and KZ were found, and suggest that this approach may be useful for providing alternative estimates of the efficiency of turbulent mixing and measures of longer-term averages of KZ than current methods provide. Testing these potential uses will require comparison of field measurements of D with time-integrated KZ values and numerical simulations.
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Narita, Fumio, Yinli Wang, Hiroki Kurita und Masashi Suzuki. „Multi-Scale Analysis and Testing of Tensile Behavior in Polymers with Randomly Oriented and Agglomerated Cellulose Nanofibers“. Nanomaterials 10, Nr. 4 (07.04.2020): 700. http://dx.doi.org/10.3390/nano10040700.
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Cellulose nanofiber (CNF) has been accepted as a valid nanofiller that can improve the mechanical properties of composite materials by mechanical and chemical methods. The purpose of this work is to numerically and experimentally evaluate the mechanical behavior of CNF-reinforced polymer composites under tensile loading. Finite element analysis (FEA) was conducted using a model for the representative volume element of CNF/epoxy composites to determine the effective Young’s modulus and the stress state within the composites. The possible random orientation of the CNFs was considered in the finite element model. Tensile tests were also conducted on the CNF/epoxy composites to identify the effect of CNFs on their tensile behavior. The numerical findings were then correlated with the test results. The present randomly oriented CNF/epoxy composite model provides a means for exploring the property interactions across different length scales.
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Zeng, Jicai, Jinzhong Yang, Yuanyuan Zha und Liangsheng Shi. „Capturing soil-water and groundwater interactions with an iterative feedback coupling scheme: new HYDRUS package for MODFLOW“. Hydrology and Earth System Sciences 23, Nr. 2 (04.02.2019): 637–55. http://dx.doi.org/10.5194/hess-23-637-2019.
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Abstract. Accurately capturing the complex soil-water and groundwater interactions is vital for describing the coupling between subsurface–surface–atmospheric systems in regional-scale models. The nonlinearity of Richards' equation (RE) for water flow, however, introduces numerical complexity to large unsaturated–saturated modeling systems. An alternative is to use quasi-3-D methods with a feedback coupling scheme to practically join sub-models with different properties, such as governing equations, numerical scales, and dimensionalities. In this work, to reduce the nonlinearity in the coupling system, two different forms of RE are switched according to the soil-water content at each numerical node. A rigorous multi-scale water balance analysis is carried out at the phreatic interface to link the soil-water and groundwater models at separated spatial and temporal scales. For problems with dynamic groundwater flow, the nontrivial coupling errors introduced by the saturated lateral fluxes are minimized with a moving-boundary approach. It is shown that the developed iterative feedback coupling scheme results in significant error reduction and is numerically efficient for capturing drastic flow interactions at the water table, especially with dynamic local groundwater flow. The coupling scheme is developed into a new HYDRUS package for MODFLOW, which is applicable to regional-scale problems.
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Vaarmann, Otu. „HIGH ORDER ITERATIVE METHODS FOR DECOMPOSITION‐COORDINATION PROBLEMS“. Technological and Economic Development of Economy 12, Nr. 1 (31.03.2006): 56–61. http://dx.doi.org/10.3846/13928619.2006.9637723.
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Many real‐life optimization problems are of the multiobjective type and highdimensional. Possibilities for solving large scale optimization problems on a computer network or multiprocessor computer using a multi‐level approach are studied. The paper treats numerical methods in which procedural and rounding errors are unavoidable, for example, those arising in mathematical modelling and simulation. For the solution of involving decomposition‐coordination problems some rapidly convergent interative methods are developed based on the classical cubically convergent method of tangent hyperbolas (Chebyshev‐Halley method) and the method of tangent parabolas (Euler‐Chebyshev method). A family of iterative methods having the convergence order equal to four is also considered. Convergence properties and computational aspects of the methods under consideration are examined. The problems of their global implementation and polyalgorithmic strategy are discussed as well.
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Düreth, Christian, Daniel Weck, Robert Böhm, Mike Thieme, Maik Gude, Sebastian Henkel, Carl Wolf und Horst Biermann. „Determining the Damage and Failure Behaviour of Textile Reinforced Composites under Combined In-Plane and Out-of-Plane Loading“. Materials 13, Nr. 21 (26.10.2020): 4772. http://dx.doi.org/10.3390/ma13214772.
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The absence of sufficient knowledge of the heterogeneous damage behaviour of textile reinforced composites, especially under combined in-plane and out-of-plane loadings, requires the development of multi-scale experimental and numerical methods. In the scope of this paper, three different types of plain weave fabrics with increasing areal weight were considered to characterise the influence of ondulation and nesting effects on the damage behaviour. Therefore an advanced new biaxial testing method has been elaborated to experimentally determine the fracture resistance at the combined biaxial loads. Methods in image processing of the acquired in-situ CT data and micrographs have been utilised to obtain profound knowledge of the textile geometry and the distribution of the fibre volume content of each type. Combining the derived data of the idealised geometry with a numerical multi-scale approach was sufficient to determine the fracture resistances of predefined uniaxial and biaxial load paths. Thereby, Cuntze’s three-dimensional failure mode concept was incorporated to predict damage and failure. The embedded element method was used to obtain a structured mesh of the complex textile geometries. The usage of statistical and visualisation methods contributed to a profound comprehension of the ondulation and nesting effects.
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Wang, Xigui, Siyuan An, Yongmei Wang, Jiafu Ruan und Baixue Fu. „Semi-numerical analysis of a two-stage series composite planetary transmission considering incremental harmonic balance and multi-scale perturbation methods“. Mechanical Sciences 12, Nr. 2 (08.07.2021): 701–14. http://dx.doi.org/10.5194/ms-12-701-2021.
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Abstract. This study conducts an analytical investigation of the dynamic response characteristics of a two-stage series composite system (TsSCS) with a planetary transmission consisting of dual-power branches. An improved incremental harmonic balance (IHB) method, which solves the closed solution of incremental parameters passing through the singularity point of the analytical path, based on the arc length extension technique, is proposed. The results are compared with those of the numerical integration method to verify the feasibility and effectiveness of the improved method. Following that, the multi-scale perturbation (MsP) method is applied to the TsSCS proposed in this subject to analyze the parameter excitation and gap nonlinear equations and then to obtain the analytical frequency response functions including the fundamental, subharmonic, and superharmonic resonance responses. The frequency response equations of the primary resonance, subharmonic resonance, and superharmonic resonance are solved to generate the frequency response characteristic curves of the planetary gear system (PGS) in this method. A comparison between the results obtained by the MsP method and the numerical integration method proves that the former is ideal and credible in most regions. Considering the parameters of TsSCS excitation frequency and damping, the nonlinear response characteristics of steady-state motion are mutually converted. The effects of the time-varying parameters and the nonlinear deenthing caused by the gear teeth clearance on the amplitude–frequency characteristics of TsSCS components are studied in this special topic.
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Imura, Makoto, Tetsusei Kurashiki, Hiroaki Nakai und Masaru Zako. „A Multi-Scale Analysis for an Evaluation of the Mechanical Properties of Composite Materials“. Key Engineering Materials 334-335 (März 2007): 585–88. http://dx.doi.org/10.4028/www.scientific.net/kem.334-335.585.
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Fiber reinforced composite materials have been applied widely to many structures, because they have some advantages like easy handling, high specific strength, etc. The numerical method like finite element method has been applied to design and to evaluate the material properties and behavior as the development of Computer Aided Engineering. It is very difficult to calculate with accuracy not only in structural scale but also in detail material scale (for example, the order of fiber diameter) by the traditional FEM, becausecompositematerials like woven fabric composites have the geometrical complexityand the large difference between above mentioned scales. The development of multi-scale analysis method is one of the major topics in computational mechanics. Mesh superpositionis one of multi-scale analysis methods and is an effective method to solve the problems which have the large difference between the structure scale and the reinforcement scale. We have expanded the finite element mesh superposition method with 3 scales and have defined as M3 (Macro-Meso-Micro) method. In this paper, we have proposed a new approach method combined with M3 method and homogenized method to obtain the mechanical properties and to simulate the behavior of woven fabric composites. In addition, the elastic-plastic mechanics and the damage mechanics have been introduced into M3 method to investigate the effects of matrix-crack on the structural and material properties. From the numerical results, it is revealed that it is very useful for the evaluation of mechanical properties of composite materials.
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HE, WEN-YU, und WEI-XIN REN. „ADAPTIVE TRIGONOMETRIC HERMITE WAVELET FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS“. International Journal of Structural Stability and Dynamics 13, Nr. 01 (Februar 2013): 1350007. http://dx.doi.org/10.1142/s0219455413500077.
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Owing to its good approximation characteristics of trigonometric functions and the multi-resolution local characteristics of wavelet, the trigonometric Hermite wavelet function is used as the element interpolation function. The corresponding trigonometric wavelet beam element is formulated based on the principle of minimum potential energy. As the order of wavelet can be enhanced easily and the multi-resolution can be achieved by the multi-scale of wavelet, the hierarchical and multi-resolution trigonometric wavelet beam element methods are proposed for the adaptive analysis. Numerical examples have demonstrated that the aforementioned two methods are effective in improving the computational accuracy. The trigonometric wavelet finite element method (WFEM) proposed herein provides an alternative approach for improving the computational accuracy, which can be tailored for the problem considered.
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Alawneh, Shadi G., Lei Zeng und Seyed Ali Arefifar. „A Review of High-Performance Computing Methods for Power Flow Analysis“. Mathematics 11, Nr. 11 (26.05.2023): 2461. http://dx.doi.org/10.3390/math11112461.
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Power flow analysis is critical for power systems due to the development of multiple energy supplies. For safety, stability, and real-time response in grid operation, grid planning, and analysis of power systems, it requires designing high-performance computing methods, accelerating power flow calculation, obtaining the voltage magnitude and phase angle of buses inside the power system, and coping with the increasingly complex large-scale power system. This paper provides an overview of the available parallel methods to fix the issues. Specifically, these methods can be classified into three categories from a hardware perspective: multi-cores, hybrid CPU-GPU architecture, and FPGA. In addition, from the perspective of numerical computation, the power flow algorithm is generally classified into iterative and direct methods. This review paper introduces models of power flow and hardware computing architectures and then compares their performance in parallel power flow calculations depending on parallel numerical methods on different computing platforms. Furthermore, this paper analyzes the challenges and pros and cons of these methods and provides guidance on how to exploit the parallelism of future power flow applications.
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Zhou, Rui, Weicheng Gao und Wei Liu. „An MMF3 Criterion Based Multi-Scale Strategy for the Failure Analysis of Plain-Woven Fabric Composites and Its Validation in the Open-Hole Compression Tests“. Materials 14, Nr. 16 (05.08.2021): 4393. http://dx.doi.org/10.3390/ma14164393.
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A modified micromechanics failure criterion (MMF3) based multi-scale analysis strategy was proposed in this article to analyze the failure behaviors of the plain-woven fabric composites. The finite-element (FE) representative unit cell (RUC) models of different scales were first established, and the RUC based stress transformation methods were developed. The micro-scale strengths of the constituents in the unidirectional laminate were achieved based on the tested macro-scale strengths. Under the micro-scale strength invariance hypothesis, the meso-scale strengths of the fiber tows from the plain-woven fabric composites were back-calculated first and were then validated and corrected with the assistance of tested strengths of the fabric laminates. With the micro-scale RUC and the calculated meso-scale strengths of the fiber tows, the micro-scale strengths of the constituents suitable for the plain-woven fabric composites were determined. The multi-scale analysis procedure for the plain-woven fabric composites was then established in providing a more direct failure observation at the constituent level. Open-hole compression specimens were tested according to the ASTM standard D6484, and the failure of the open-hole fabric laminate was simulated with the proposed multi-scale strategy. The numerical predictions were in good agreement with the experimental results, and the feasibility of the multi-scale strategy was validated.
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Wang, Xinsheng, Chenxu Wang und Mingyan Yu. „The Minimum Norm Least-Squares Solution in Reduction by Krylov Subspace Methods“. Journal of Circuits, Systems and Computers 26, Nr. 01 (04.10.2016): 1750006. http://dx.doi.org/10.1142/s0218126617500062.
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In recent years, model order reduction (MOR) of interconnect system has become an important technique to reduce the computation complexity and improve the verification efficiency in the nanometer VLSI design. The Krylov subspaces techniques in existing MOR methods are efficient, and have become the methods of choice for generating small-scale macro-models of the large-scale multi-port RCL networks that arise in VLSI interconnect analysis. Although the Krylov subspace projection-based MOR methods have been widely studied over the past decade in the electrical computer-aided design community, all of them do not provide a best optimal solution in a given order. In this paper, a minimum norm least-squares solution for MOR by Krylov subspace methods is proposed. The method is based on generalized inverse (or pseudo-inverse) theory. This enables a new criterion for MOR-based Krylov subspace projection methods. Two numerical examples are used to test the PRIMA method based on the method proposed in this paper as a standard model.
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Haussener, Sophia. „(Invited, Digital Presentation) Transport Characterization in Nano and Micron-Sized Multi-Component and Multi-Functional Materials“. ECS Meeting Abstracts MA2022-01, Nr. 38 (07.07.2022): 1649. http://dx.doi.org/10.1149/ma2022-01381649mtgabs.
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Porous and heterogeneous materials are core components in energy conversion and storage devices such as batteries, fuel cells and electrolyzers, or photoelectrochemical fuel generators. The heterogeneity and structural complexity of: i) the multi-functional nature of the applications requiring the presence of various functional materials in close vicinity, ii) nano- and micron-scale structuring of the material required to overcome the bulk material transport limitations, and iii) cheap and simple synthesis methods resulting in stochastic and complex morphologies. Understanding of the multi-physical transport phenomena and optimization of the component for enhanced performance, requires an accurate modelling and prediction of the transport properties, which heavily rely on the complex nano to micron-scale morphology. In this presentation, I will show how tomography-based direct numerical simulation scan be used for the accurate numerical characterization of the heterogeneous components’ transport properties. We will use X-ray micro-tomography for the characterization of the (thermal) transport in partially saturated gas diffusion layers/electrodes or in porous thermochemical reactors, and FIB-SEM nano-tomography for the multi-physical transport characterization of photoelectordes for water splitting and catalyst layers of CO2 reducing gas diffusion electrodes. I will show how we have built up a digital library of (photo)electrodes. Furthermore, I will show how machine learning approaches can be used to guide the design of optimized structures.
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Siow, Chyan Zheng, Azhar Aulia Saputra, Takenori Obo und Naoyuki Kubota. „A Fast Multi-Scale of Distributed Batch-Learning Growing Neural Gas for Multi-Camera 3D Environmental Map Building“. Biomimetics 9, Nr. 9 (16.09.2024): 560. http://dx.doi.org/10.3390/biomimetics9090560.
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Biologically inspired intelligent methods have been applied to various sensing systems in order to extract features from a huge size of raw sensing data. For example, point cloud data can be applied to human activity recognition, multi-person tracking, and suspicious person detection, but a single RGB-D camera is not enough to perform the above tasks. Therefore, this study propose a 3D environmental map-building method integrating point cloud data measured via multiple RGB-D cameras. First, a fast multi-scale of distributed batch-learning growing neural gas (Fast MS-DBL-GNG) is proposed as a topological feature extraction method in order to reduce computational costs because a single RGB-D camera may output 1 million data. Next, random sample consensus (RANSAC) is applied to integrate two sets of point cloud data using topological features. In order to show the effectiveness of the proposed method, Fast MS-DBL-GNG is applied to perform topological mapping from several point cloud data sets measured in different directions with some overlapping areas included in two images. The experimental results show that the proposed method can extract topological features enough to integrate point cloud data sets, and it runs 14 times faster than the previous GNG method with a 23% reduction in the quantization error. Finally, this paper discuss the advantage and disadvantage of the proposed method through numerical comparison with other methods, and explain future works to improve the proposed method.
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Bian, Ye, Chengyong Si und Lei Wang. „Diabetic Retinopathy Lesion Segmentation Method Based on Multi-Scale Attention and Lesion Perception“. Algorithms 17, Nr. 4 (19.04.2024): 164. http://dx.doi.org/10.3390/a17040164.
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The early diagnosis of diabetic retinopathy (DR) can effectively prevent irreversible vision loss and assist ophthalmologists in providing timely and accurate treatment plans. However, the existing methods based on deep learning have a weak perception ability of different scale information in retinal fundus images, and the segmentation capability of subtle lesions is also insufficient. This paper aims to address these issues and proposes MLNet for DR lesion segmentation, which mainly consists of the Multi-Scale Attention Block (MSAB) and the Lesion Perception Block (LPB). The MSAB is designed to capture multi-scale lesion features in fundus images, while the LPB perceives subtle lesions in depth. In addition, a novel loss function with tailored lesion weight is designed to reduce the influence of imbalanced datasets on the algorithm. The performance comparison between MLNet and other state-of-the-art methods is carried out in the DDR dataset and DIARETDB1 dataset, and MLNet achieves the best results of 51.81% mAUPR, 49.85% mDice, and 37.19% mIoU in the DDR dataset, and 67.16% mAUPR and 61.82% mDice in the DIARETDB1 dataset. The generalization experiment of MLNet in the IDRiD dataset achieves 59.54% mAUPR, which is the best among other methods. The results show that MLNet has outstanding DR lesion segmentation ability.
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Krejčí, Tomáš, Aleš Jíra, Luboš Řehounek, Michal Šejnoha, Jaroslav Kruis und Tomáš Koudelka. „Homogenization of trabecular structures“. MATEC Web of Conferences 310 (2020): 00041. http://dx.doi.org/10.1051/matecconf/202031000041.
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Numerical modeling of implants and specimens made from trabecular structures can be difficult and time-consuming. Trabecular structures are characterized as spatial truss structures composed of beams. A detailed discretization using the finite element method usually leads to a large number of degrees of freedom. It is attributed to the effort of creating a very fine mesh to capture the geometry of beams of the structure as accurately as possible. This contribution presents a numerical homogenization as one of the possible methods of trabecular structures modeling. The proposed approach is based on a multi-scale analysis, where the whole specimen is assumed to be homogeneous at a macro-level with assigned effective properties derived from an independent homogenization problem at a meso-level. Therein, the trabecular structure is seen as a porous or two-component medium with the metal structure and voids filled with the air or bone tissue at the meso-level. This corresponds to a two-level finite element homogenization scheme. The specimen is discretized by a reasonable coarse mesh at the macro-level, called the macro-scale problem, while the actual microstructure represented by a periodic unit cell is discretized with sufficient accuracy, called the meso-scale problem. Such a procedure was already applied to modeling of composite materials or masonry structures. The application of this multi-scale analysis is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.
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dos Santos, Ronaldo Medeiros, Sérgio Koide, Bruno Esteves Távora und Daiana Lira de Araujo. „Groundwater Recharge in the Cerrado Biome, Brazil—A Multi-Method Study at Experimental Watershed Scale“. Water 13, Nr. 1 (24.12.2020): 20. http://dx.doi.org/10.3390/w13010020.
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Groundwater recharge is a key hydrological process for integrated water resource management, as it recharges aquifers and maintains the baseflow of perennial rivers. In Brazil, the Cerrado biome is an important continental recharge zone, but information on rates and spatial distribution is still lacking for this country. The objective of this work was to characterize the groundwater recharge process in phreatic aquifers of the Cerrado biome. For this, an experimental watershed representative of the referred biome was established and intensively monitored. The methodology consisted of an inverse numerical modeling approach of the saturated zone and three classic methods of recharge evaluation—hydrological modeling, baseflow separation, and water table elevation. The results indicated average potential recharge around 35% of the annual precipitation, average effective recharge around 21%, and higher rates occurring in flat areas of Ferralsols covered with natural vegetation of the Cerrado biome. As the level of uncertainty inferred from the methods was high, these results were considered a first attempt and will be better evaluated by comparison with other methods not applied in this work, such as the lysimeter and chemical tracer methods.
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Comişel, H., Y. Narita und U. Motschmann. „Wavevector anisotropy of plasma turbulence at ion kinetic scales: solar wind observations and hybrid simulations“. Nonlinear Processes in Geophysics 21, Nr. 6 (11.11.2014): 1075–83. http://dx.doi.org/10.5194/npg-21-1075-2014.
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Abstract. Wavevector anisotropy of ion-scale plasma turbulence is studied at various values of ion beta. Two complementary methods are used. One is multi-point measurements of magnetic field in the near-Earth solar wind as provided by the Cluster spacecraft mission, and the other is hybrid numerical simulation of two-dimensional plasma turbulence. Both methods demonstrate that the wavevector anisotropy is reduced with increasing values of ion beta. Furthermore, the numerical simulation study shows the existence of a scaling law between ion beta and the wavevector anisotropy of the fluctuating magnetic field that is controlled by the thermal or hybrid particle-in-cell simulation noise. Likewise, there is weak evidence that the power-law scaling can be extended to the turbulent fluctuating cascade. This fact can be used to construct a diagnostic tool to determine or to constrain ion beta using multi-point magnetic field measurements in space.