人工边界方法 英文版
作者：韩厚德，巫孝南 著
出版时间：2012年版
内容简介
人工边界方法是求解无界区域上偏微分方程（组）数值解的一个重要和有效的方法。人工边界方法的核心问题是在人工边界上如何对已知的问题找出问题的解满足的准确（或者高精度近似）的边界条件。借助于人工边界方法，我们可将无界区域上的问题简化为有界区域上的问题进行数值计算。《Artificial Boundary Method(人工边界方法)(精)(英文)》系统地介绍了人工边界方法的计算格式及其理论基础。《Artificial Boundary Method(人工边界方法)(精)(英文)》可以作为科学与工程计算专业研究生课程的教材，亦可以作为科学与工程计算专业科学技术人员的参考书。
目 录
introduction
references
chapter 1 global abcs for second order elliptic equations
1.1 exterior problem of second order elliptic equations
1.2 global abcs for the exterior problem of 2-d poissonequation
1.2.1 steklov-poincaré mapping for the exterior problem of laplaceequation
1.2.2 the reduced boundary value problem oni.
1.2.3 finite element approximation of the reduced boundary valueproblem (1.2.30)~(1.2.32)
1.3 global abcs for the exterior problems of 3-d poissonequation
1.3.1 exact and approximate abcs on the spherical artificialboundary γr
1.3.2 equivalent and approximate boundary value problems on thebounded computational domaini
1.3.3 finite element approximation of the variational problem(1.3.30)
1.4 exterior problem of the modified helmholtz equation
1.4.1 global boundary condition of the exterior problem for the 2-dmodified helmholtz equation
1.4.2 the reduced boundary value problem on the computationaldomaini
1.4.3 finite element approximation of the reduced boundary valueproblem
1.4.4 global boundary condition of the exterior problem for the 3-dmodified helmholtz equation
1.5 global abcs for the exterior problems of the helmholtzequation
1.5.1 dirichlet to sommerfeld mapping of the exterior problem ofthe 2-d helmholtz equation
1.5.2 dirichlet to sommerfeld mapping of the exterior problem ofthe 3-d helmholtz equation
references
chapter 2 global abcs for the navier system and stokessystem
2.1 navier system and stokes system
2.2 the exterior problem of the 2-d navier system
2.2.1 the global boundary condition on the artificial boundaryγr
2.2.2 the reduced problem on the bounded domain
2.2.3 the finite element approximation for the reduced problem(2.2.59)
2.3 exterior problem of the 2-d stokes system
2.3.1 highly accurate approximate artificial boundarycondition
2.3.2 finite element approximation on the computational domaini forthe reduced problem
2.4 vector fields on the spherical surface.
2.5 global abcs for the exterior problem of 3-d naviersystem.
2.5.1 highly accurate approximate abcs
2.5.2 finite element approximation of the variational problem onthe bounded computational domaini 100 references
chapter 3 global abcs for heat and schr.dinger equations
3.1 heat equations on unbounded domains
3.2 1-d heat equations on unbounded domains
3.2.1 exact boundary conditions on the artificial boundary σ
3.2.2 finite difference approximation for the reduced problem(3.2.7)~(3.2.10)
3.2.3 stability analysis of scheme (3.2.29)~(3.2.33)
3.3 global boundary conditions for exterior problems of 2-d heatequations
3.3.1 exact and approximate conditions on the artificial boundaryσr.
3.3.2 finite difference approximation of the reduced problem(3.3.37)~(3.3.40)
3.4 global boundary conditions for exterior problems of 3-d heatequations
3.4.1 exact and approximate conditions on the artificial boundaryσr.
3.4.2 stability analysis for the reduced initial boundary valueproblem
3.4.3 the finite element approximation for the reduced initialboundary value problem (3.4.38)~(3.4.41)
3.5 schr.dinger equation on unbounded domains
3.6 1-d schr.dinger equation on unbounded domains.
3.6.1 the reduced initial value problem and its finite differenceapproximation
3.6.2 stability and convergence analysis of scheme(3.6.19)~(3.6.22)
3.7 the global boundary condition for the exterior problem of the2-d linear schr.dinger equation
3.7.1 exact and approximate boundary conditions on the artificialboundary σr
3.7.2 stability analysis of the reduced approximate initialboundary value problem
3.8 the global boundary condition for the exterior problem of the3-d linear schr.dinger equation
3.8.1 exact and approximate boundary conditions on the artificialboundary σr
3.8.2 stability analysis of the reduced approximate initialboundary value problem
references
chapter 4 abcs for wave equation, klein-gordon equation, andlinear kdv equations
4.1 1-d wave equation
4.1.1 transparent boundary conditions on the artificial boundariesσ1 and σ
4.2 2-d wave equation
4.2.1 absorbing boundary conditions
4.2.2 the initial boundary value problem on the boundedcomputational domain di
4.3 3-d wave equation
4.3.1 absorbing boundary condition on the artificial boundaryσr
4.3.2 the equivalent and approximate initial boundary value problemon the bounded computational domain di
4.4 1-d klein-gordon equation
4.4.1 absorbing boundary conditions on the artificial boundary σ1,σ
4.4.2 the initial boundary value problem on the boundedcomputational domain di
4.5 2- and 3-d klein-gordon equations.
4.5.1 absorbing boundary conditions on the artificial boundary σr(2-d case)
4.5.2 absorbing boundary conditions on the artificial boundary σr(3-d case)
4.5.3 the initial boundary value problem on the boundedcomputational domain di
4.6 linear kdv equation
4.6.1 absorbing boundary condition on the artificial boundaries σaand σb
4.6.2 the equivalent initial boundary value problem on the boundedcomputational domain
4.7 appendix: three integration formulas
references
chapter 5 local artificial boundary conditions
5.1 local boundary conditions for exterior problems of the 2-dpoisson equation
5.1.1 local boundary condition on the artificial bboundary γr
5.1.2 finite element approximation using the local boundarycondition and its error estimate
5.2 local boundary conditions for the 3-d poisson equation
5.2.1 the local boundary condition on the artificial boundary γrfor problem (i)
5.2.2 local boundary conditions on the artificial boundary γr forproblem (ii)
5.3 local abcs for wave equations on unbounded domains
references
chapter 6 discrete artificial boundary conditions
6.1 boundary condition on a polygon boundary for the 2-d poissonequation—the method of lines
6.1.1 discrete boundary conditions on polygonal boundaries
6.1.2 numerical approximation of the exterior problem(6.1.1)~(6.1.3)
6.2 2-d viscous incompressible flow in a channel—infinitedifference method
6.2.1 2-d viscous incompressible flow in a channel
6.2.2 discrete abcs
6.3 numerical simulation of infinite elastic foundation—infiniteelement method
6.3.1 the steklov-poincarè on an artificial boundary of linesegments
6.3.2 numerical approximation for the bilinear form b(u, v)
6.3.3 a direct method for solving the infinite system of algebraicequations (6.3.25)
6.3.4 a fast iteration method for computing the combined stiffnessmatrix kz.
6.4 discrete absorbing boundary condition for the 1-d klein-gordonequation—z transform method
6.4.1 z transform
6.4.2 discrete absorbing abc
6.4.3 finite difference approximation for the 1-d klein-gordonequation on the bounded domain.296 references
chapter 7 implicit artificial boundary conditions
7.1 implicit boundary condition for the exterior problem of the 2-dpoisson equation
7.1.1 the single and double layer potential, and their derivativefor the 2-d laplace equation
7.1.2 the derivation of the implicit abc for the exterior problemof the 2-d poisson equation
7.1.3 the finite element approximation and error estimate for thevariational problem (7.1.37)
7.2 implicit boundary condition for the exterior problem of the 3-dpoisson equation
7.3 abc for the exteriorproblem of the helmholtz equation
7.3.1 the normal derivative on γa for the double layer potential ofthe helmholtz equation
7.4 implicit abcs for the exterior problems of the naviersystem.
7.4.1 fundamental solution, stress operator, single and doublelayer potentials
7.4.2 new forms of t(.x, nx)vii (x) on γa (n = 2)
7.4.3 new forms of t(.x, nx)vii (x) on γa (n = 3)
7.4.4 implicit abc for the exterior problem
7.5 implicit abcs for the sound wave equation.
7.5.1 the kirchhoff formula for the 3-d sound wave equation
references
chapter 8 nonlinear artificial boundary conditions
8.1 the burgers equation
8.1.1 nonlinear abcs for the burgers equation
8.1.2 the equivalent initial boundary value problem on the boundedcomputational domain di
8.2 the kardar-parisi-zhang equation
8.2.1 nonlinear abc for the k-p-z equation (d = 1)
8.2.2 nonlinear abc for the k-p-z equation (d = 2)
8.2.3 nonlinear abc for the k-p-z equation (d = 3)
8.3 the cubic nonlinear schr.dinger equation.
8.3.1 nonlinear boundary conditions on the artificial boundaries σ0and σ.
8.3.2 the equivalent initial boundary value problem on the boundeddomain [–1, 0] × [0, t ]
8.4 operator splitting method for constructing approximatenonlinear abcs
8.4.1 the local absorbing abc for the linear schr.dingerequation
8.4.2 finite difference approximation on the bounded computationaldomain.360 references
chapter 9 applications to problems with singularity
9.1 the modified helmholtz equation with a singularity
9.1.1 abc near singular points
9.1.2 an iteration method based on the abc
9.2 the interface problem with a singularity
9.2.1 a discrete boundary condition on the artificial boundaryγr
9.2.2 finite element approximation
9.3 the linearelastic problem with asingularity
9.3.1 discrete boundary condition on the artificial boundaryγr
9.3.2 an iteration method based on the abc
9.4 the stokes equations with a singularity
9.4.1 the discrete boundary condition on the artificial boundaryγr
9.4.2 singular finite element approximation
references
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