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1.
一维对流扩散方程CRANK—NICOLSON特征差分格式 总被引:10,自引:0,他引:10
本文针对一维线性和非线性对流扩散方程提出一种Crank-Nicolson类型的特征差分格式,给出了该格式形成的线性代数方程组可解的一个充条件,证明了该格式按离散L^2模是收敛的,且其收敛阶为O(△t^ h^2). 相似文献
2.
We examine the convergence characteristics of a preconditioned Krylov subspace solver applied to the linear systems arising
from low-order mixed finite element approximation of the biharmonic problem. The key feature of our approach is that the preconditioning
can be realized using any “black-box” multigrid solver designed for the discrete Dirichlet Laplacian operator. This leads
to preconditioned systems having an eigenvalue distribution consisting of a tightly clustered set together with a small number
of outliers. Numerical results show that the performance of the methodology is competitive with that of specialized fast iteration
methods that have been developed in the context of biharmonic problems.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
Grigory I. Shishkin 《高等学校计算数学学报(英文版)》2008,1(2):214-234
A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation;we construct a finite difference scheme on a priori (se-quentially) adapted meshes and study its convergence.The scheme on a priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution,which allows us to find a priori a subdomain where the computed solution requires a further improvement.This subdomain is defined by the perturbation parameterε,the step-size of a uniform mesh in x,and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for im- proving the solution.To solve the discrete problems aimed at the improvement of the solution,we use uniform meshes on the subdomains.The error of the numerical so- lution depends weakly on the parameterε.The scheme converges almostε-uniformly, precisely,under the condition N~(-1)=o(ε~v),where N denotes the number of nodes in the spatial mesh,and the value v=v(K) can be chosen arbitrarily small for suitable K. 相似文献
4.
This paper proposes and analyzes a class of multigrid smoothers called the parallel multiplicative (PM) smoother by subspace decomposition techniques. It shows that the well known additive and multiplicative smoothers and the JSOR smoother are special cases of the PM smoother, and their smoothing properties can be obtained directly from the PM analysis. Moreover, numerical results are presented in this paper to show that the JSOR smoother is more robust and effective than the damped Jacobi smoother on current MIMD parallel computers.
AMS subject classification (2000) 65N55, 65Y05.Received May 2004. Revised September 2004. Communicated by Per Lötstedt.Dexuan Xie: This work was partially supported by the National Science Foundation through grant DMS-0241236. 相似文献
5.
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
6.
汪玥 《数学的实践与认识》2012,42(9):154-161
提出了一种求解线性和非线性对流扩散方程的流函数松弛方法.方法的主要思想是利用流函数松弛近似将原始的方程转化成等价的松弛方程组,新的松弛方程组是带源项的双曲系统.通过稳定性分析可以知道新系统的耗散系数可由松弛系数调整.数值实现亦证明这个方法可以快速有效地描述对流扩散方程的解. 相似文献
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Lunji Song Yujiang Wu 《高等学校计算数学学报(英文版)》2007,16(1):14-27
We use the incremental unknowns method in conjunction with the iterative methods to approximate the solution of the nonsymmetric and positive-definite linear systems generated from a multilevel discretization of three-dimensional convection-diffusion equations. The condition numbers of incremental unknowns matrices associated with the convection-diffusion equations and the number of iterations needed to attain an acceptable accuracy are estimated. Numerical results are presented with two-level approximations, which demonstrate that the incremental unknowns method when combined with some iter- ative methods is very effcient. 相似文献
9.
为了改进求解大型稀疏线性互补问题模系多重网格方法的收敛速度和计算时间,本文采用加速模系超松弛(AMSOR)迭代方法作为光滑算子.局部傅里叶分析和数值结果表明此光滑算子能有效地改进模系多重网格方法的收敛因子、迭代次数和计算时间. 相似文献
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Eugene O'Riordan Jeanne Stynes Martin Stynes 《高等学校计算数学学报(英文版)》2008,1(2):176-197
A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds. 相似文献
12.
介绍了对流扩散方程的混合有限分析法 ,得出了求解对流扩散方程隐式格式、离散算子 ,并且证明了这些格式解的存在性 ,分析了格式的截断误差 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
15.
给出求解一种二维非线性对流扩散方程组的 Grank-Nicolson型特征有限元方法 ,并给出该方法的 H1模最优阶误差估计 . 相似文献
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Zhong-ciShi Xue-junXu Hong-yingMan 《计算数学(英文版)》2004,22(6):905-920
In this paper, some effective cascadic multigrid methods are proposed for solving the large scale symmetric or nonsymmetric algebraic systems arising from the finite volume methods for second order elliptic problems. It is shown that these algorithms are optimal in both accuracy and computational complexity. Numerical experiments are reported to support our theory. 相似文献
18.
In this paper, standard and economical cascadic multigrid methods are con-sidered for solving the algebraic systems resulting from the mortar finite element meth-ods. Both cascadic multigrid methods do not need full elliptic regularity, so they can be used to tackle more general elliptic problems. Numerical experiments are reported to support our theory. 相似文献
19.
A multigrid scheme for the solution of constrained optimal control problems discretized by finite differences is presented. This scheme is based on a new relaxation procedure that satisfies the given constraints pointwise on the computational grid. In applications, the cases of distributed and boundary control problems with box constraints are considered. The efficient and robust computational performance of the present multigrid scheme allows to investigate bang-bang control problems.AMS Subject Classification: 49J20, 65N06, 65N12, 65N55Supported in part by the SFB 03 “Optimization and Control” 相似文献
20.
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