共查询到20条相似文献,搜索用时 718 毫秒
1.
2.
3.
本文主要讨论求解高波数Helmholtz方程的多水平方法,主要回顾了一些具有代表性的多重网格方法.如Erlangga等人的shifted Laplacian预处理的多重网格法;Elman等提出的修正的多重网格方法;以及我们的基于连续内罚有限元(CIP-FEM)离散代数系统的多水平算法.最后还介绍了求解高波数时谐Maxwell方程的CIP-FEM离散代数系统的多水平算法. 相似文献
4.
本文考虑了一种求解大Reynolds数定常Navier-Stokes方程带回溯(backtracking)技巧的两水平有限元方法.其基本思想是,首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上求解一个亚格子模型稳定化的线性Newton问题,最后又回到粗网格上求解线性化的校正问题.通过适当的稳定化参数和粗细网格尺寸的选取,本文的算法能取得最优渐近收敛阶.数值实验检验了理论分析的正确性和算法的有效性. 相似文献
5.
多介质大变形流动数值模拟的关键和难点是在精确追踪物质界面的同时又能够处理好流体的大变形运动.将MOF(moment-of-fluid)界面重构算法与多介质任意Lagrange-Euler方法(MMALE)相耦合,形成MOF-MMALE方法,并应用于多介质大变形流动问题的数值模拟研究.MOF-MMALE方法在传统的ALE方法基础上,允许计算网格边界跨过物质界面,允许存在混合网格,即一个网格内可以存在两种或两种以上物质;在混合网格内,利用MOF界面重构算法来确定物质界面的位置和方向.数值算例表明,MOF-MMALE方法是模拟多介质大变形流动的有效手段,并且具有较好的数值精度和界面分辨率. 相似文献
6.
《应用数学与计算数学学报》2017,(4)
提出了求解两同心球所介区域上Allen-Cahn型方程的时间方向二阶精度的混合Chebyshev-Legendre-球面调和拟谱格式,即在半径方向选择混合Chebyshev-Legendre插值逼近,球面方向选择球面调和插值逼近,而时间方向的导数采用二阶中心差商离散.数值结果显示该算法具有很高精度. 相似文献
7.
主要研究了一类非线性对流扩散方程的全离散特征有限元方法的两重网格算法及其误差估计.首先在网格步长为H的粗网格上计算一个较小的非线性问题,然后利用一阶牛顿迭代和粗网格解将网格步长为h的细网格上的非线性问题转化为线性问题求解.由于非线性问题的求解仅在粗网格上进行,该两重网格算法可以节省大量的计算工作量,同时具有较高的精度,证明了该两重网格算法L~2模先验误差估计结果为O(△t+h~2+H~(4-d/2)),其中d为空间维数. 相似文献
8.
利用Riemann解的通量差分分裂法——Godunov方法对Oseen流控制方程进行离散,得到了基于一阶上迎风格式的离散方程,并给出了使用多重网格方法求解该离散方程的V-循环算法和W-循环算法的收敛性分析.通过局部Fourier分析方法,对获得的离散方程的聚对称交替线GaussSeidel松弛的光滑性质进行了研究.结果表明:使用多重网格的两层网格及三层网格算法求解具有不同Reynolds数的Oseen流,即便是在高Reynolds数情况下,聚对称交替线Gauss-Seidel松弛具有很好的光滑性质,多重网格W-循环算法收敛性比V-循环算法好. 相似文献
9.
《数学的实践与认识》2020,(17)
提出了一种受偏微分方程约束最优控制问题的移动网格方法,并以NavierStokes方程为状态方程进行了研究.所采用的网格移动策略中节点距离的移动是通过求解一个扩散方程得到.设计出了有效的求解流体力学最优控制问题的算法,给出了算法的实施过程.提供的数值算例说明所提算法可以在保证高精度数值解的前提下稳定、高效的求解最优控制问题. 相似文献
10.
11.
The efficient generation of meshes is an important component in the numerical
solution of problems in physics and engineering. Of interest are situations where
global mesh quality and a tight coupling to the solution of the physical partial differential
equation (PDE) is important. We consider parabolic PDE mesh generation
and present a method for the construction of adaptive meshes in two spatial dimensions
using stochastic domain decomposition that is suitable for an implementation
in a multi- or many-core environment. Methods for mesh generation on periodic domains
are also provided. The mesh generator is coupled to a time dependent physical
PDE and the system is evolved using an alternating solution procedure. The method
uses the stochastic representation of the exact solution of a parabolic linear mesh generator
to find the location of an adaptive mesh along the (artificial) subdomain interfaces.
The deterministic evaluation of the mesh over each subdomain can then be
obtained completely independently using the probabilistically computed solutions as
boundary conditions. A small scaling study is provided to demonstrate the parallel
performance of this stochastic domain decomposition approach to mesh generation.
We demonstrate the approach numerically and compare the mesh obtained with the
corresponding single domain mesh using a representative mesh quality measure. 相似文献
12.
Victoria Hernández-Mederos Pedro L. del Ángel Jorge Estrada-Sarlabous 《Numerical Algorithms》2008,48(1-3):29-47
In this paper we propose an advancing front method for generating an isotropic triangular mesh on a regular parametric surface. Starting from a point on the surface, the method computes a set of points in the intersection curve between the surface and the sphere centered at that point with a prescribed radius. From this set we select the vertices of a cell composed by triangles approximately equilateral. The mesh grows repeating the described computation with boundary vertices of the cell as starting points. Compared to methods proposed by other authors, the current method may be considered as an improvement, since it is more efficient and flexible. Furthermore, the resulting mesh is closer to being isotropic. Additionally, we obtain a sufficient condition ensuring that a surface triangulation is of Delaunay type. 相似文献
13.
We present a new mesh simplification technique developed for a statistical analysis of a large data set distributed on a generic complex surface, topologically equivalent to a sphere. In particular, we focus on an application to cortical surface thickness data. The aim of this approach is to produce a simplified mesh which does not distort the original data distribution so that the statistical estimates computed over the new mesh exhibit good inferential properties. To do this, we propose an iterative technique that, for each iteration, contracts the edge of the mesh with the lowest value of a cost function. This cost function takes into account both the geometry of the surface and the distribution of the data on it. After the data are associated with the simplified mesh, they are analyzed via a spatial regression model for non-planar domains. In particular, we resort to a penalized regression method that first conformally maps the simplified cortical surface mesh into a planar region. Then, existing planar spatial smoothing techniques are extended to non-planar domains by suitably including the flattening phase. The effectiveness of the entire process is numerically demonstrated via a simulation study and an application to cortical surface thickness data. 相似文献
14.
陈志祥 《应用泛函分析学报》2010,12(1):33-38
X是S2的有限子集,它的网格范数为hX.文章利用分析工具对hX的上、下界估计进行了一些研究和探讨.同时给出了所得结果在球面数值分析与逼近中的具体应用. 相似文献
15.
J. Southern G.J. Gorman M.D. Piggott P.E. Farrell M.O. Bernabeu J. Pitt-Francis 《Journal of computational science》2010,1(2):82-88
The simulation of cardiac electrophysiology requires small time steps and a fine mesh in order to resolve very sharp, but highly localized, wavefronts. The use of very high resolution meshes containing large numbers of nodes results in a high computational cost, both in terms of CPU hours and memory footprint. In this paper an anisotropic mesh adaptivity technique is implemented in the Chaste physiological simulation library in order to reduce the mesh resolution away from the depolarization front. Adapting the mesh results in a reduction in the number of degrees of freedom of the system to be solved by an order of magnitude during propagation and 2–3 orders of magnitude in the subsequent plateau phase. As a result, a computational speedup by a factor of between 5 and 12 has been obtained with no loss of accuracy, both in a slab-like geometry and for a realistic heart mesh with a spatial resolution of 0.125 mm. 相似文献
16.
空间半无界区域的非重叠区域分解算法 总被引:1,自引:0,他引:1
主要研究了空间一种半无界凹球区域上的区域分解算法.在三维空间自然边界规划的基础上,以三维Dirichlet外边值问题为例,进行的D-N交替算法.并提出了该算法与Richardson迭代法的等价性,并分析其收敛性及其收敛速度与网格参数h无关.同时给出了松弛因子的取值范围. 相似文献
17.
An adaptive method is developed for solving one-dimensional systems of hyperbolic conservation laws, which combines the rezoning approach with the finite volume weighted essentially non-oscillatory (WENO) scheme. An a posteriori error estimate, used to equidistribute the mesh, is obtained from the differences between respective numerical solutions of 5th-order WENO (WENO5) and 3rd-order ENO (ENO3) schemes. The number of grids can be adaptively readjusted based on the solution structure. For higher efficiency, mesh readjustment is performed every few time steps rather than every time step. In addition, a high order conservative interpolation is used to compute the physical solutions on the new mesh from old mesh based on the finite volume ENO reconstruction. Extensive examples suggest that this adaptive method exhibits more accurate resolution of discontinuities for a similar level of computational time comparing with that on a uniform mesh. 相似文献
18.
Daniel Ruprecht 《PAMM》2014,14(1):1031-1034
The effect is investigated of using a reduced spatial resolution in the coarse propagator of the time-parallel Parareal method for a finite difference discretization of the linear advection-diffusion equation. It is found that convergence can critically depend on the order of the interpolation used to transfer the coarse propagator solution to the fine mesh in the correction step. The effect also strongly depends on the employed spatial and temporal resolution. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
In this paper, we discuss multiscale radial basis function collocation methods for solving certain elliptic partial differential
equations on the unit sphere. The approximate solution is constructed in a multi-level fashion, each level using compactly
supported radial basis functions of smaller scale on an increasingly fine mesh. Two variants of the collocation method are
considered (sometimes called symmetric and unsymmetric, although here both are symmetric). A convergence theory is given,
which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. 相似文献
20.
Goal of this paper is to suitably combine a model with an anisotropic mesh adaptation
for the numerical simulation of nonlinear advection-diffusion-reaction systems and incompressible flows
in ecological and environmental applications.
Using the reduced-basis method terminology, the proposed approach leads to a noticeable computational saving of the online phase
with respect to the resolution of the reference model on nonadapted grids.
The search of a suitable adapted model/mesh pair is to be meant, instead, in an offline fashion. 相似文献