共查询到19条相似文献,搜索用时 78 毫秒
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抛物问题非协调元多重网格法 总被引:6,自引:0,他引:6
抛物问题非协调元多重网格法周叔子,文承标(湖南大学应用数学系)NONCONFORMINGELEMENTMULTIGRIDMETHODFORMRABOLICEQUATIONS¥ZhouShu-zi;WenCheng-biao(HunanUniversi... 相似文献
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Huo-Yuan Duan Shao-Qin Gao Roger C. E. Tan Shangyou Zhang. 《Mathematics of Computation》2007,76(257):137-152
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and it produces a variable V-cycle, or nonuniform convergence rate V-cycle methods, or other nonoptimal results in analysis thus far.
This paper completes a long-time effort in extending the BPX multigrid framework so that it truly covers the nonnested V-cycle. We will apply the extended BPX framework to the analysis of many V-cycle nonnested multigrid methods. Some of them were proven previously only for two-level and W-cycle iterations. Some numerical results are presented to support the theoretical analysis of this paper.
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Here two types of optimal V-cycle multigrid algorithms are presented for Wilson nonconforming finite element. 相似文献
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半线性椭圆型问题Mortar有限元逼近的瀑布型多重网格法 总被引:1,自引:0,他引:1
Mortar有限元法作为一个非协调的区域分解技术已得到许多研究者的关注(如文献[2]、[5]等)。本文对半线性椭圆型问题的Mortar有限元逼近提出了瀑布型多重网格法,并给出了此法的误差估计和计算复杂度估计定理。 相似文献
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Chun-jiaBi Li-kangLi 《计算数学(英文版)》2004,22(1):123-136
The purpose of this paper is to study the cascadic multigrid method for the secondorder elliptic problems with curved boundary in two-dimension which are discretized by the isoparametric finite element method with numerical integration. We show that the CCG method is accurate with optimal complexity and traditional multigrid smoother (likesymmetric Gauss-Seidel, SSOR or damped Jacobi iteration) is accurate with suboptimal complexity. 相似文献
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用瀑布型多重网格法解决椭圆、抛物问题,已有不少研究工作[1-2],本文对抛物问题的mortar有限元的全离散格式提出瀑布型多重网格法,证明了该方法是最优的,即具有最优精确度和复杂度. 相似文献
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Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function 下载免费PDF全文
Aicha Driouch & Hassan Al Moatassime 《数学研究》2020,53(3):247-264
This paper deals with the task of pricing European basket options in the presence of transaction costs. We develop a model that incorporates the illiquidity of
the market into the classical two-assets Black-Scholes framework. We perform a numerical simulation using finite difference method. We consider a nonlinear multigrid
method in order to reduce computational costs. The objective of this paper is to investigate a deterministic extension for the Barles' and Soner's model and to demonstrate
the effectiveness of multigrid approach to solving a fully nonlinear two dimensional
Black-Scholes problem. 相似文献
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The purpose of this work is to reduce the CPU time necessary to solve three two-dimensional linear diffusive problems governed by Laplace and Poisson equations, discretized with anisotropic grids. The Finite Difference Method is used to discretizate the differential equations with central differencing scheme. The systems of equations are solved with the lexicographic and red–black Gauss–Seidel methods associated to the geometric multigrid with correction scheme and V-cycle. The anisotropic grids considered have aspect ratios varying from 1/1024 up to 16,384. Four algorithms are compared: full coarsening, semicoarsening, full coarsening followed by semicoarsening and partial semicoarsening. Three new restriction schemes for anisotropic grids are proposed: geometric half weighting, geometric full weighting and partial weighting. Comparisons are made among these three new schemes and some restriction schemes presented in literature: injection, half weighting and full weighting. The prolongation process used is the bilinear interpolation. It is also investigated the effects on the CPU time caused by: the number of inner iterations of the smoother, the number of grids and the number of grid elements. It was verified that the partial semicoarsening algorithm is the fastest. This work also provides the optimum values of the multigrid components for this algorithm. 相似文献