ISBN-10:
9812705260
ISBN-13:
9789812705266
Pub. Date:
02/28/2007
Publisher:
World Scientific Publishing Company, Incorporated
Numerical Methods for Exterior Problems

Numerical Methods for Exterior Problems

by Lung-an Ying

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Overview

Numerical Methods for Exterior Problems

This book provides a comprehensive introduction to the numerical methods for the exterior problems in partial differential equations frequently encountered in science and engineering computing. The coverage includes both traditional and novel methods. A concise introduction to the well-posedness of the problems is given, establishing a solid foundation for the methods.

Product Details

ISBN-13: 9789812705266
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 02/28/2007
Series: Peking University Series In Mathematics Series
Pages: 280
Product dimensions: 6.00(w) x 8.90(h) x 0.70(d)

Table of Contents


Preface     v
Exterior Problems of Partial Differential Equations     1
Harmonic equation-potential theory     2
Poisson equations     12
Poisson equations-variational formulation     13
Helmholtz equations     17
Linear elasticity     25
Bi-harmonic equations     29
Steady-Navier-Stokes equations -linearized problems     35
Navier-Stokes equations     35
Stokes equations     36
Behavior of solutions at the infinity     39
Stokes paradox     41
Oseen flow     41
Steady Navier-Stokes equations     44
Heat equation     49
Wave equation     53
Maxwell equations     56
Darwin model     61
Boundary Element Method     71
Some typical domains     71
Harmonic equation     71
Bi-harmonic equation     75
Stokes equation     77
Plane elasticity     80
Helmholtz equation     82
General domains     85
Subdivision of the domain     93
Dirichlet to Neumann operator     96
Finite part of divergentintegrals     98
Numerical approximation     103
Error estimates     108
Domain decomposition     113
Boundary perturbation     114
Infinite Element Method     117
Harmonic equation-two dimensional problems     117
Infinite element formulation     117
Tranfer matrix     120
Further discussion for the transfer matrix     127
Combined stiffness matrix     131
General elements     133
Harmonic equation-three dimensional problems     134
Inhomogeneous equations     136
Plane elasticity     138
Bi-harmonic equations     140
Stokes equation     142
Darwin model     147
Elliptic equations with variable coefficients     152
A homogeneous equation     152
An inhomogeneous equation     155
General multiply connected domains     158
Transfer matrices     161
Convergence     162
Artificial Boundary Conditions     167
Absorbing boundary conditions     167
Some approximations     172
Bayliss-Turkel radiation boundary conditions     175
A lower order absorbing boundary condition     176
Liao extrapolation in space and time     178
Maxwell equations     178
Finite difference schemes     182
Stationary Navier-Stokes equations     183
Homogeneous boundary condition at the infinity     183
Inhomogeneous boundary conditions at the infinity     186
A linear boundary condition     187
Perfectly Matched Layer Method     191
Wave equations     191
Berenger's perfectly matched layers     197
Stability analysis     201
Uniaxial perfectly matched layers     208
Maxwell equations     210
Helmholtz equations     212
Spectral Method     217
Introduction     217
Orthogonal systems of polynomials     225
Laguerre spectral methods     230
Mixed Laguerre-Fourier spectral method     230
Spherical harmonic-generalized Laguerre spectral method     235
Generalized Laguerre pseudo-spectral method     237
Nonlinear equations     239
Jacobi spectral methods     241
Rational and irrational spectral methods     243
Error estimates      245
Bibliography     251
Index     265

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