Description 
1 online resource 
Series 
Peking University series in mathematics ; v. 2 

Peking University series in mathematics ; v. 2

Contents 
Preface  1. Exterior problems of partial differential equations. 1.1. Harmonic equationpotential theory. 1.2. Poisson equations. 1.3. Poisson equationsvariational formulation. 1.4. Helmholtz equations. 1.5. Linear elasticity. 1.6. Biharmonic equations. 1.7. Steady NavierStokes equationslinearized problems. 1.8. Steady NavierStokes equations. 1.9. Heat equation. 1.10. Wave equation. 1.11. Maxwell equations. 1.12. Darwin model  2. Boundary element method. 2.1. Some typical domains. 2.2. General domains. 2.3. Subdivision of the domain. 2.4. Dirichlet to Neǔmann operator. 2.5. Finite part of divergent integrals. 2.6. Numerical approximation. 2.7. Error estimates. 2.8. Domain decomposition. 2.9. Boundary perturbation  3. Infinite element method. 3.1. Harmonic equationtwo dimensional problems. 3.2. General elements. 3.3. Harmonic equationthree dimensional problems. 3.4. Inhomogeneous equations. 3.5. Plane elasticity. 3.6. Biharmonic equations. 3.7. Stokes equation. 3.8. Darwin model. 3.9. Elliptic equations with variable coefficients. 3.10. Convergence  4. Artificial boundary conditions. 4.1. Absorbing boundary conditions. 4.2. Some approximations. 4.3. BaylissTurkel radiation boundary conditions. 4.4. A lower order absorbing boundary condition. 4.5. Liao extrapolation in space and time. 4.6. Maxwell equations. 4.7. Finite difference schemes. 4.8. Stationary NavierStokes equations  5. Perfectly matched layer method. 5.1. Wave equations. 5.2. Bérenger's perfectly matched layers. 5.3. Stability analysis. 5.4. Uniaxial perfectly matched layers. 5.5. Maxwell equations. 5.6. Helmholtz equations  6. Spectral method. 6.1. Introduction. 6.2. Orthogonal systems of polynomials. 6.3. Laguerre spectral methods. 6.4. Jacobi spectral methods. 6.5. Rational and irrational spectral methods. 6.6. Error estimates 
Summary 
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 wellposedness of the problems is given, establishing a solid foundation for the methods. Sample Chapter(s). Chapter 1: Exterior Problems of Partial Differential Equations (1,839 KB). Contents: Exterior Problems of Partial Differential Equations; Boundary Element Method; Infinite Element Method; Artificial Boundary C 
Bibliography 
Includes bibliographical references (pages 251263) and index 
Subject 
Differential equations, Partial.

Form 
Electronic book

ISBN 
9789812772565 (electronic bk.) 

9812772561 (electronic bk.) 
