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81.
Séraphin M.Mefire 《计算数学(英文版)》2005,23(2):131-152
A numerical method combining the approaches of C.I. Goldstein and L.-A. Ying is used for the simulation in three-dimensional magnetostatics related to an exterior problem in magnetic induction. Recently introduced, this method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain and has been performed in the case of edge element discretizations. In this work, the theoretical and practical aspects of the method are inspected in the case of face element and volume element discretizations,for computing a magnetic induction. Error estimates, implementations, and numerical results are provided. 相似文献
82.
Integration factor methods are a class of “exactly linear part” time discretization methods. In [Q. Nie, Y.-T. Zhang, R. Zhao, Efficient semi-implicit schemes for stiff systems, Journal of Computational Physics, 214 (2006) 521–537], a class of efficient implicit integration factor (IIF) methods were developed for solving systems with both stiff linear and nonlinear terms, arising from spatial discretization of time-dependent partial differential equations (PDEs) with linear high order terms and stiff lower order nonlinear terms. The tremendous challenge in applying IIF temporal discretization for PDEs on high spatial dimensions is how to evaluate the matrix exponential operator efficiently. For spatial discretization on unstructured meshes to solve PDEs on complex geometrical domains, how to efficiently apply the IIF temporal discretization was open. In this paper, we solve this problem by applying the Krylov subspace approximations to the matrix exponential operator. Then we apply this novel time discretization technique to discontinuous Galerkin (DG) methods on unstructured meshes for solving reaction–diffusion equations. Numerical examples are shown to demonstrate the accuracy, efficiency and robustness of the method in resolving the stiffness of the DG spatial operator for reaction–diffusion PDEs. Application of the method to a mathematical model in pattern formation during zebrafish embryo development shall be shown. 相似文献
83.
In this paper,a new proof of superclose of a Crouzeix-Raviart type finite element is given for second order elliptic boundary value problem by Bramble-Hilbert lemma on anisotropic meshes. 相似文献
84.
A refined r‐factor algorithm for implementing total variation diminishing (TVD) schemes on arbitrary unstructured meshes, referred to henceforth as a face‐perpendicular far‐upwind interpolation scheme for arbitrary meshes (FFISAM), is proposed based on an extensive review of the existing r‐factor algorithms available in the literature. The design principles, as well as the respective advantages and disadvantages, of the existing algorithms are first systematically analyzed before presenting the FFISAM. The FFISAM is designed to combine the merits of various existing r‐factor algorithms. The performance of the FFISAM, implemented in 10 classical TVD schemes, is evaluated against four two‐dimensional pure‐advection benchmark test cases where analytical solutions are available. The numerical results clearly show that the FFISAM leads to a better overall performance than the existing algorithms in terms of accuracy and convergence on arbitrary unstructured meshes for the 10 classical TVD schemes. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
85.
Yan-Qun Jiang · Ru-Xun Liu · Ya-Li Duan Department of Mathematics Southwest University of Science Technology Mianyang China Department of Mathematics University of Science Technology of China Hefei China 《Acta Mechanica Sinica》2011,27(2):215-221
In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians. 相似文献
86.
A method for computing curved meshes via the linear elasticity analogy,application to fluid dynamics problems 下载免费PDF全文
We propose and analyze an algorithm for the robust construction of curved meshes in two and three dimensions. The meshes are made of curved simplexes. The algorithm starts from a mesh made of straight simplexes, and using a linear elasticity analogy applied on well‐chosen data, one can generate a curved mesh. Note that if the initial mesh has a boundary layer, this method allows to conserve it on the final mesh. This algorithm is used on several airfoils in two and three dimensions, including a turbulent M6 wing. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
87.
A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection. 相似文献
88.
通过摄动系数建立分层网格,用多尺度有限元法捕捉对流扩散方程的两端边界层,研究二维奇异摄动模型。基于分层网格并利用多尺度基函数刻画了边界层的微观信息,用有限的计算资源、较短的计算时间,得到了不依赖于摄动系数、一致稳定的模拟结果。 相似文献
89.
Júlia Mingot Nícolas Benejam Gloria Víllora Carlos Alemán Elaine Armelin Sonia Lanzalaco 《Macromolecular bioscience》2023,23(7):2300118
This work presents a novel nanoparticle-based thermosensor implant able to reveal the precise temperature variations along the polymer filaments, as it contracts and expands due to changes in the macroscale local temperature. The multimodal device is able to trace the position and the temperature of a polypropylene mesh, employed in abdominal hernia repair, by combining plasmon resonance and Raman spectroscopy with hydrogel responsive system. The novelty relies on the attachment of the biocompatible nanoparticles, based on gold stabilized by a chitosan-shell, already charged with the Raman reporter (RaR) molecules, to the robust prosthesis, without the need of chemical linkers. The SERS enhanced effect observed is potentiated by the presence of a quite thick layer of the copolymer (poly(N-isopropylacrylamide)-co-poly(acrylamide)) hydrogel. At temperatures above the LCST of PNIPAAm-co-PAAm, the water molecules are expulsed and the hydrogel layer contracts, leaving the RaR molecules more accessible to the Raman source. In vitro studies with fibroblast cells reveal that the functionalized surgical mesh is biocompatible and no toxic substances are leached in the medium. The mesh sensor opens new frontiers to semi-invasive diagnosis and infection prevention in hernia repair by using SERS spectroscopy. It also offers new possibilities to the functionalization of other healthcare products. 相似文献
90.
This paper presents a posteriori residual error estimator for the new mixed element scheme for second order elliptic problem on anisotropic meshes. The reliability and efficiency of our estimator are established without any regularity assumption on the mesh. 相似文献