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Non- symmetric indefinite second order elliptic boundary value problems multigrid convergence

Author: LuoZhiQiang
Tutor: ZhongErJie
School: University of Electronic Science and Technology
Course: Computational Mathematics
Keywords: Multigrid methods V- cycle convergence Error iterations Non - symmetric indefinite Elliptic Boundary Value Problems
CLC: O175.25
Type: Master's thesis
Year: 2005
Downloads: 58
Quote: 1
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Abstract


In this paper, a second-order elliptic boundary value problems coordinating the convergence of the finite element multigrid V- cycle . Symmetric positive definite elliptic boundary value problems have been many research symmetric positive definite elliptic boundary value problems error attenuation . Finite element space will coordinate decomposed into a the frequency subspace low frequency subspace of straight and , thus the error attenuation changes translate into high considering the changes in attenuation of high-frequency and low-frequency component of the error on the low - frequency subspace . The further observation error in the orthogonal subspace polished smooth iterations and coarse-grid correction effect relationship , and estimate the convergence factor is less than 1 . The second chapter is the research carried out in this context , and focuses on the grid function space orthogonal subspace error polished effect , the degree of attenuation of the error and convergence analysis . Coordination of multi-grid finite element method approximate solution of symmetric positive definite elliptic boundary value problems , often the solution , smooth sub regular approximation assumptions , under the premise of no regular weak assumptions , we reduce direct derivation of error count the sub convergence relationship , the third chapter analyzes the symmetric positive definite elliptic boundary value problems , multigrid V- cycle convergence . In this paper, considering the non - symmetric indefinite elliptic boundary value problems in the low-order terms of the coefficient is not very large case . relationship , combined with the given assumptions and Lemma , concise analysis of the non- symmetric indefinite elliptic boundary value problems of second-order V- cycle convergence . Regular assumptions Richardson iterative scheme , non - symmetric indefinite second order elliptic boundary value problems multigrid methods convergence . In the fifth chapter , through the establishment of certain weak assumptions , the derivation of some important theorems proved in the regular assumptions under the premise of non- symmetric indefinite second order elliptic boundary value problems multigrid V- cycle convergence .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Elliptic equations
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