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References (22)
-
M. Dryja (1982)
A capacitance matrix method for Dirichlet problem on polygon regionNumerische Mathematik, 39
-
J. Bramble, J. Pasciak, A. Schatz (1986)
An iterative method for elliptic problems on regions partitioned into substructuresMathematics of Computation, 46
-
名取 亮, 野寺 隆 (1986)
Conjugate gradient method and its applications -
P. Bjørstad, O. Widlund (1984)
SOLVING ELLIPTIC PROBLEMS ON REGIONS PARTITIONED INTO SUBSTRUCTURES -
A. Abakumov, A. Yeremin, Y. Kuznetsov (1988)
Efficient fast direct method of solving Poisson’s equation on a parallelepiped and its implementation in an array processor, 3
-
B. Il'in (1976)
Some estimates for conjugate gradient methodsUssr Computational Mathematics and Mathematical Physics, 16
-
(1985)
Computational methods in subspaces -
(1976)
D'yakonov, Some classes of spectrally equivalent operators and their applications -
G. Golub, D. Mayers (1983)
The use of pre-conditioning over irregular regions -
(1984)
Bjorstad and O . Widlund , Solving elliptic problem on regions partitioned into substructures -
(1979)
D'yakonov, On some direct and iterative methods based on matrix bordering -
V. Andreev (1972)
Stability of finite-difference schemes for elliptic equations with respect to Dirichlet boundary conditionsUssr Computational Mathematics and Mathematical Physics, 12
-
(1971)
on-Homogeneous Boundary Value Problems and Its Applications -
(1984)
Matrix computational processes in subspaces In: Comp -
(1966)
D'yakonov, On construction of iterative methods using spectrally equivalent operators, Zh -
J. Pasciak, A. George, Joseph Liu (1982)
Computer solution of large sparse positive definite systemsMathematics of Computation, 39
-
(1983)
Application of bordering to solve systems of mesh equations. In: Computational Algorithms in Problems of Mathematical Physics. Novosibirsk, Vychisi -
Fictitious components domain and domain decomposition methods -
(1976)
D'Leary, A generalized conjugate gradient method for numerical solution of elliptic partial differential equations. In: Sparse Matrix Computation -
(1975)
Matsokin, On construction and methods for systems of variational-difference equations -
(1986)
Domain decomposition and the Schwartz method in a subspace for approximate solution of elliptic boundary value problems, Ph. D. Thesis, Novosibirsk, Vychisi -
(1979)
Block relaxation methods in a subspace to solve two-dimensional elliptic equations
- Publisher
- de Gruyter
- Copyright
- Copyright © 2009 Walter de Gruyter
- ISSN
- 0927-6467
- eISSN
- 1569-3988
- DOI
- 10.1515/rnam.1988.3.4.245
- Publisher site
- See Article on Publisher Site
Abstract
Abstract--The paper suggests a new approach to construction of preconditioned and convergence rate estimates for iterative methods to solve simultaneous linear algebraic equations arising in finite element approximations of elliptic problems. The approach is based on the decomposition of the original mesh domain into superelements. It is proved that for many important practical problems the convergence rate estimates of the methods considered do not depend on the mesh, and also on coefficients and boundary conditions of the original differential problem. INTRODUCTION Let be a bounded two-dimensional polygonal domain with the boundary , and let 0 be a closed subset of <3 consisting of a finite number of straight line segments. Following [19] define the Sobolev space Hl = W\(Q) and its subspace v = Qon 0}. In particular, if 0 = , then V = Hj = $\(\ and if 0 = 0, we have V = Hl. If mes 0 > 0, the relation /3 2 dQ 1 1 / 2 3 3 J J defines in the space V a norm which is equivalent to the Hl-norm and in the case where f = 0, the relation ioHUnlA *!/ + hr~ (o-i \ *2/ f &
Journal
Russian Journal of Numerical Analysis and Mathematical Modelling – de Gruyter
Published: Jan 1, 1988