Numerical Methods For Exterior Problems

By: Lung-an Ying

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Paperback | 22 November 2006

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280 Pages

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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.

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

At a Glance

Paperback

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