Infinite element methods
著者
書誌事項
Infinite element methods
Peking University Press , Vieweg Publishing, c1995
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注記
Bibliography: p. [205]-209
内容説明・目次
内容説明
In the infinite element method, the underlying domain is divided into infinitely many pieces. This leads to a system of infinitely many equations for infinitely many unknowns, but these can be reduced by analytical technicians to a finite system when some sort of scaling is present in the original problem. The simplest illustrative example, described carefully at the beginning of the first chapter of the book, is the solution of the Dirichlet problem in the exterior of some polygon. The exterior is subdivided into annular regions by a sequence of geometrically expanding images of the given polygon; these annuli are then further subdivided. The resulting variational equations take for the form of a block tridiagonal Toeplittz matrix, with an inhomogeneous term in the zero componenet. Various efficient methods are described for solving such systems of equations. The infinite element method is, wherever applicable, an elegant and efficient approach to solving problems in physics and engineering.
目次
- Part 1: two-dimensional exterior problems of the Laplace equation
- Fourier methods
- iterative methods
- general elements
- three-dimensional exterior problems of the Laplace equation
- problems on other unbounded domains
- corner problems
- nonhomogeneous equations and nonhomogeneous boundary conditions
- plane elasticity problems
- calculation of stress intensity factors. Part 2: foundations of algorithm
- infinite element spaces
- shift matrices
- further discussion for the infinite element spaces and the shift matrices
- shift matrices for the plane elasticity problems
- combined stiffness matrices
- structure of general solutions
- block circular stiffness matrices
- iterative method of the first type
- iterative method of the second type
- general elliptic systems
- exterior Stokes problems
- nonhomogeneous equations and the Helmholtz equation. Part 3: Some auxiliary inequalities
- approximate properties of piecewise polynomials
- H1 and L2 convergence
- a superconvergence estimate
- term-by-term convergence near the corner. Part 4 boundary value problems and Eigenvalue problems
- stress intensity factors
- Stokes external flow
- Navier-Stokes external flow.
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