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1.
We discuss the possible shapes and stress distributions of an inextensible membrane acted on by a gravitational force. It is shown that there are smooth shapes which cannot be an equilibrium solution under gravity for any stress distribution. In addition there are infinitely many shapes which are equilibrium solutions under gravity and for which the stress distribution is unique. Finally, there are infinitely many solution surfaces – each consisting of straight line generators parallel to the direction of gravity. These solutions are possible under infinitely many different stress distributions. In several cases we will solve the equations explicitly to find actual shapes and stress distributions.
Mathematics Subject Classifications (2000) 74. 相似文献
2.
In this paper, the dual integral formulation is derived for the modified Helmholtz equation in the propagation of oblique incident wave passing a thin barrier (zero thickness) by employing the concept of fast multipole method (FMM) to accelerate the construction of an influence matrix. By adopting the addition theorem, the four kernels in the dual formulation are expanded into degenerate kernels that separate the field point and the source point. The source point matrices decomposed in the four influence matrices are similar to each other or only to some combinations. There are many zeros or the same influence coefficients in the field point matrices decomposed in the four influence matrices, which can avoid calculating the same terms repeatedly. The separable technique reduces the number of floating‐point operations from O((N)2) to O(N loga(N)), where N is the number of elements and a is a small constant independent of N. Finally, the FMM is shown to reduce the CPU time and memory requirement, thus enabling us to apply boundary element method (BEM) to solve water scattering problems efficiently. Two‐moment FMM formulation was found to be sufficient for convergence in the singular equation. The results are compared well with those of conventional BEM and analytical solutions and show the accuracy and efficiency of the FMM. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
3.
Luigi Genovese Brice Videau Matthieu Ospici Thierry Deutsch Stefan Goedecker Jean-François Méhaut 《Comptes Rendus Mecanique》2011,339(2-3):149-164
In this contribution we will describe in detail a Density Functional Theory method based on a Daubechies wavelets basis set, named BigDFT. We will see that, thanks to wavelet properties, this code shows high systematic convergence properties, very good performances and an excellent efficiency for parallel calculations. BigDFT code operation are also well-suited for GPU acceleration. We will discuss how the problematic of fruitfully benefit of this new technology can be match with the needs of robustness and flexibility of a complex code like BigDFT. This work may be of interest not only for expert in electronic structure calculations, but may also provide feedback to the wider community of high performance scientific computing. 相似文献
4.
Shi Jin Peter Minev Krishnaswamy Nandakumar 《International Journal of Computational Fluid Dynamics》2013,27(5):427-437
Particulate flow is of great importance from both the scientific and engineering points of view. Owing to the complexity of particle-flow interactions, direct numerical simulations (DNS) of inertial particulate flow with finite-size particles have been limited to a very small number of particles, while the industrial applications involve larger numbers with many orders of magnitude. This article presents a parallel implementation of a fictitious domain method for the DNS of particulate flows. The method is thoroughly tested and its parallel performance on distributed memory clusters is evaluated on a large-scale problem. Finally, we present the results for the separation of 21,336 particles of two different densities in a viscous fluid. Although there is still a significant gap between DNS and the industrial applications, the present algorithm allows to simulate significantly large number of particles so that a meaningful statistical analysis can be performed. This will help in the development of new closure relations for the averaged models of multiphase flows. 相似文献
5.
并行计算机和计算流体力学并行算法 总被引:6,自引:0,他引:6
对研制计算流体力学高效并行算法及软件具有重要意义的并行计算问题提出了导引性的看法.首先综述了并行计算机的主要设计特征并简要描述了市场现有的几种并行系统.接着介绍了一些有关研制并行算法及评价其性能的重要概念.然后讨论了如何使分布式内存并行计算机的运行负载不平衡和通信开销达到最小.最后列举了计算流体力学某些算例的测试结果.本文的重点是结构网格和分程序结构网格的应用,但这些概念和方法对非结构网格同样有效 相似文献
6.
The total solution of a three-dimensional model for computing the transport of salinity, pollutants, suspended material (such as sediment or mud), etc. in shallow seas involves many aspects, each of which has to be treated in an optimal way in order to cope with the tremendous computational task involved. In this paper we focus on one of these aspects, i.e. on the time integration, and discuss two numerical solution methods. The emphasis in this paper is on the performance of the methods when implemented on a vector/parallel, shared memory computer such as a Cray-type machine. The first method is an explicit time integrator and can straightforwardly be vectorized and parallelized. Although a stabilizing technique has been applied to this method, it still suffers from a severe time step restriction. The second method is partly implicit, resulting in much better stability characteristics; however, as a consequence of the implicitness, it requires in each step the solution of a large number of tridiagonal systems. When implemented in a standard way, the recursive nature would prevent vectorization, resulting in a very long solution time. Following a suggestion of Golub and Van Loan, this part of the algorithm has been tuned for use on the Cray C98/4256. On the basis of a large-scale test problem, performance results will be presented for various implementations. 相似文献
7.
The total solution of a three-dimensional model for computing the transport of salinity, pollutants, suspended material (such as sediment or mud), etc. in shallow seas involves many aspects, each of which has to be treated in an optimal way in order to cope with the tremendous computational task involved. In this paper we focus on one of these aspects, i.e. on the time integration, and discuss two numerical solution methods. The emphasis in this paper is on the performance of the methods when implemented on a vector/parallel, shared memory computer such as a Cray-type machine. The first method is an explicit time integrator and can straightforwardly be vectorized and parallelized. Although a stabilizing technique has been applied to this method, it still suffers from a severe time step restriction. The second method is partly implicit, resulting in much beter stability characteristics; however, as a consequence of the implicitness, it requires in each step the solution of a large number of tridiagonal systems. When implemented in a standard way, the recursive nature would prevent vectorization, resulting in a very long solution time. Following a suggestion of Golub and Van Loan, this part of the algorithm has been tuned for use on the Cray C98/4256. On the basis of a large-scale test problem, performance results will be presented for various implementations. 相似文献
8.
9.
Performance analysis of a 3D unstructured mesh hydrodynamics code on multi‐core and many‐core architectures 下载免费PDF全文
J. Waltz J. G. Wohlbier L. D. Risinger T. R. Canfield M. R. J. Charest A. R. Long N. R. Morgan 《国际流体数值方法杂志》2015,77(6):319-333
Several next generation high performance computing platforms are or will be based on the so‐called many‐core architectures, which represent a significant departure from commodity multi‐core architectures. A key issue in transitioning large‐scale simulation codes from multi‐core to many‐core systems is closing the serial performance gap, that is, overcoming the large difference in single‐core performance between multi‐core and many‐core systems. In this paper, we discuss how this problem was addressed for a 3D unstructured mesh hydrodynamics code, describe how Amdahl's law can be used to estimate performance targets and guide optimization efforts, and present timing studies performed on multi‐core and many‐core platforms. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. 相似文献
10.
The method of regularized Stokeslets (MRS) uses a radially symmetric blob function of infinite support to smooth point forces and allows for evaluation of the resulting flow field. This is a common method to study swimmers at zero Reynolds number where the Stokeslet is the fundamental solution corresponding to the kernel of the single layer potential. Simulating the collective motion of N micro-swimmers using the MRS results in at least N2 pair-wise interactions. Efficient simulation of a large number of swimmers in free space is observed with the implementation of the kernel-independent fast multipole method (FMM) for radial basis functions. We illustrate the complexity of the algorithm on a simple test case where we study regularized point forces, showing that the method is of order N. Additionally, we explore accuracy in time for the MRS where the swimmers are modeled as Kirchhoff rods and the kernel-independent FMM is compared to the direct calculation using the standard MRS. Optimal hydrodynamic efficiency is also explored for different configurations of swimmers. 相似文献
11.
PARALLEL COMPUTING FOR STATIC RESPONSE ANALYSIS OF STRUCTURES WITH UNCERTAIN-BUT-BOUNDED PARAMETERS 总被引:2,自引:0,他引:2
The vertex solution for estimation on the static displacement bounds of structures with uncertain-but-bounded parameters is studied in this paper. For the linear static problem, when there are uncertain interval parameters in the stiffness matrix and the vector of applied forces, the static response may be an interval. Based on the interval operations, the interval solution obtained by the vertex solution is more accurate and more credible than other methods (such as the perturbation method). However, the vertex solution method by traditional serial computing usually needs large computational efforts, especially for large structures. In order to avoid its disadvantages of large calculation and much runtime, its parallel computing which can be used in large-scale computing is presented in this paper. Two kinds of parallel computing algorithms are proposed based on the vertex solution. The parallel computing will solve many interval problems which cannot be resolved by traditional interval analysis methods. 相似文献
12.
《Wave Motion》2016
This paper discusses an FMM for solving waveguide problems and associated eigenvalue problems for Helmholtz’ equation in a two dimensional infinite strip with homogeneous Neumann boundary condition on the sides. Layer potentials with Green’s function for this problem are evaluated efficiently with the help of the method of images and FMM. We apply FMM to solve some boundary value problems in waveguides and associated resonance frequency problems using the Sakurai–Sugiura projection method after discussing the required analytic continuation of the solutions to complex frequencies. Some numerical examples show the accuracy and the efficiency of the proposed method. 相似文献
13.
This article is mainly devoted to a review on fast BEMs for elastodynamics, with particular attention on time-harmonic fast multipole methods (FMMs). It also includes original results that complete a very recent study on the FMM for elastodynamic problems in semi-infinite media. The main concepts underlying fast elastodynamic BEMs and the kernel-dependent elastodynamic FM-BEM based on the diagonal-form kernel decomposition are reviewed. An elastodynamic FM-BEM based on the half-space Green’s tensor suitable for semi-infinite media, and in particular on the fast evaluation of the corresponding governing double-layer integral operator involved in the BIE formulation of wave scattering by underground cavities, is then presented. Results on numerical tests for the multipole evaluation of the half-space traction Green’s tensor and the FMM treatment of a sample 3D problem involving wave scattering by an underground cavity demonstrate the accuracy of the proposed approach. The article concludes with a discussion of several topics open to further investigation, with relevant published work surveyed in the process. 相似文献
14.
This paper treats a liquid-metal flow through a simple manifold connecting one duct to two parallel ducts. The manifold consists
of an infinitely long, constant-area, rectangular duct with a uniform, transverse magnetic field and with a semi-infinite
middle wall at the plane of symmetry which is perpendicular to the magnetic field. The magnetic flux density is sufficiently
large that inertial effects can be neglected everywhere and that viscous effects are confined to boundary layers and to an
interior layer along the magnetic field lines through the end of the middle wall. The purpose of this paper is to illustrate
an approach with eigenfunction expansions which will be useful for manifolds with many parallel ducts. In the present simple
manifold, the principal three-dimensional effect is a transfer of flow to the inviscid core region from the high-velocity
jets adjacent to the sides which are parallel to the magnetic field. There is also an important redistribution of flow along
magnetic field lines inside the side-wall boundary layers. 相似文献
15.
Adam Frank Jonathan Carroll Eric G. Blackman Fabian Heitsch Sergey Lebedev 《High Energy Density Physics》2013,9(2):341-346
In this contribution we present new simulations of colliding flows relevant to star formation studies which may also be relevant to future HEDLA experiments. We first discuss AstroBEAR a multi-physics MHD AMR code whose functionality and parallel performance make it a highly useful tool for star formation studies. We then present the results of two simulations of colliding flows that only differed with regards to the degree of inhomogeneity. One flow was completely uniform (Smooth), while the other contained many small over-densities in a lighter background (Clumpy) though with the same mean density, mass flux, & ram pressure. Despite these similarities, the two runs differed significantly with regards to their overall evolution, mixing, and core formation. The Smooth run formed cores early on throughout the cloud – while the inhomogeneities present in the Clumpy run drove a higher degree of small scale turbulence which seemed able to prevent local collapse. The Clumpy run did form cores but only after global collapse had ensued at around 20 Myr. The Smooth run managed to avoid global collapse for the duration of the simulation due to the increased splashing of material radially outwards as well as the higher pressure of the incoming material due to the details of the heating/cooling curve. In the final section we comment on possible applications of these studies to future HEDLA experiments. We conclude that key aspects of the flow evolution before gravitational collapse sets in may be amenable to laboratory studies. 相似文献
16.
A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites 总被引:2,自引:0,他引:2
In this paper, an adaptive boundary element method (BEM) is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method (FMM) and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element (RVE) for short fiber-reinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.The project supported by the National Natural Science Foundation of China (10472051).The English text was polished by Yunming Chen. 相似文献
17.
A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) and the Type II singularity analysis of a quadratic 4-DOF 3T1R (SCARA) parallel manipulator: the Quadrupteron. It will be proved that there exists a one-to-one correspondence between the two formulas, each producing one solution to the FDA, and the two singularity-free regions. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-free region in which it works is specified. The Type II singularity analysis in the joint space will also be investigated in order to identify the conditions on the inputs to keep the Quadrupteron working in the same singularity-free region in its Cartesian workspace. 相似文献
18.
Huang Si-xun 《应用数学和力学(英文版)》1987,8(9):853-860
In this paper we discuss discontinuous periodic solution and discontinuous solitary wave of the shallow water model of geophysical fluid dynamics. When we consider the properties of trajectory near non-equilibrium point, i.e. singular point, we find that if we introduce the concept of generalized solution (piecewise smoothing continuous solution), then the system will produce discontinues periodic solution and the condition of discontinuous periodic solution can he obtained. When the system is degenerated, we find that the discontinuous solitary wave is existent in the system. In this paper we consider a series of problems and obtain analytic expression of discontinuous solution. This result is compared with squall line in the atmosphere, and both of them have many things in common. 相似文献
19.
在虚边界元最小二乘法的方程求解中采用新型的快速多极展开和广义极小残值法,提出了一种二维弹性新型快速多极虚边界元最小二乘法的求解思想。基于二维弹性问题原有的快速多极虚边界元最小二乘法的展开格式,通过引入对角化的概念,以更新展开传递格式;相对于原有快速多极算法,该方法可进一步提高计算效率且仍能保证具有较高的计算精度。数值算例说明了该方法的可行性、计算效率、计算精度均较高。 相似文献