区域分解算法

所属分类:数学  
出版时间:2006-1   出版时间:科学出版社   作者:托塞尔   页数:450   字数:551000  
Tag标签:国外数学名著经典  

内容概要

本书的目的是全面讲述偏微分方程中的各种最成功、最通用的区域分解方法,有限元逼近和谱元素逼近预条件算子,内容上做到白包含,而主要侧重点在于算法和数学方面。本书详细阐述的一些重要的方法如FETI、平衡Neumann-Neumann方法、谱元素方法等,都是第一次在数学专著中出现。

书籍目录

1
Introduction
1.1
Basic
Ideas
of
Domain
Decomposition
1.2
Matrix
and
Vector
Representations
1.3
Nonoverlapping
Methods
1.4
The
Schwarz
Alternating
Method
1.5
Block
Jacobi
Preconditioners
1.6
Some
Results
on
Schwarz
Alternating
Methods2
Abstract
Theory
of
Schwarz
Methods
2.1
Introduction
2.2
Schwarz
Methods
2.3
Convergence
Theory
2.4
Historical
Remarks
2.5
Additional
Results
2.6
Remarks
on
the
Implementation3
Two-Level
Overlapping
Methods
3.1
Introduction
3.2
Local
Solvers
3.3
A
Coarse
Problem
3.4
Scaling
and
Quotient
Space
Arguments
3.5
Technical
Tools
3.6
Convergence
Results
3.7
Remarks
on
the
Implementation
3.8
Numerical
Results
3.9
Restricted
Schwarz
Algorithms
3.10
Alternative
Coarse
Problems4
Substructruing
Methods:
Introduction
4.1
Introduction
4.2
Problem
Setting
and
Geometry
4.3
Schur
Complement
Systems
4.4
Discrete
Harmonic
Extensions
4.5
Condition
Number
of
the
Schur
Complement
4.6
Technical
Tools5
Primal
Iterative
Substructuring
Methods
5.1
Introduction
5.2
Local
Design
and
Analysia
5.3
Local
Solvers
5.4
Coarse
Spaces
and
Condition
Number
Estimates6
Neumann-Neumann
and
FETI
Methods
6.1
Introduction
6.2
Balancing
Neumann-Neumann
Methods
6.3
One-Level
FETI
Methods
6.4
Dual-Primal
FETI
Methods7
Spectral
Element
Methods
7.1
Introduction
7.2
Deville-Mund
Preconditioners
7.3
Two-Level
Overlapping
Schwarz
Methods
7.4
Iterative
Substructuring
Methods
7.5
Remarks
on
p
and
hp
Approximations8
Linear
Elasticity
8.1
Introduction
8.2
A
Two-Level
Overlapping
Method
8.3
Iterative
Substructuring
Methods
8.4
A
Wire
Basket
Based
Method
8.5
Neumann-Neumann
and
FETI
Methods9
Preconditioners
for
Saddle
Point
Problems
9.1
Introduction
9.2
Bolck
Preconditioners
9.3
Flows
in
Porous
Media
9.4
The
Stokes
Problem
and
Almost
Incompressible
Elasticity10
Problems
in
H(div;
)and
H
(curl;)
10.1
Overlapping
Methods
10.2
Iterative
Substructuring
Methods11
Indefinite
and
Nonsymmetric
Problems
11.1
Introduction
11.2
Algorithms
on
Overlapping
Subregions
11.3
An
Iterative
Substructuring
Method
11.4
Numerical
Results
11.5
Additional
TopicsA
Elliptic
Problems
and
Sobolev
Spaces
A.1
Sobolev
Spaces
A.2
Trace
Spaces
A.3
Linear
Operators
A.4
Poincare
and
Friedrichs
Type
Inequalities
A.5
Spaces
of
Vector-Valued
Functions
A.6
Positive
Definite
Problems
A.7
Non-Symmetric
and
Indefinite
Problems
A.8
Regularity
ResultsB
Galerkin
Approximations
B.1
Finite
Element
Approximations
B.2
Spectral
Element
Approximations
B.3
Divergence
and
Curl
Conforming
Finite
Elements
B.4
Saddle-Point
Problems
B.5
Inverse
Inequalities
B.6
Matrix
Representation
and
Condition
NumberC
Solution
of
Algebraic
Linear
Systemse
C.1
Eigenvalues
and
Condition
Number
C.2
Direct
Methods
C.3
Richardson
Method
C.4
Steepest
Descent
C.5
Conjugate
Gradient
Method
C.6
Methods
for
Non-Symmetric
and
Indefinite
SystemsReferencesIndex

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用户评论 (总计21条)

 
 

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