Computational and Analytic Methods in Science and Engineering

Preface......Page 5
Contents......Page 6
Contributors......Page 8
1.1 Introduction......Page 10
1.1.1 Contribution......Page 11
1.2.1 The Boundary Element Method......Page 12
Handling of the Singular Kernel......Page 13
Exploiting Symmetries of the Domain......Page 15
1.2.2 Beyn\'s Contour Integral Method......Page 17
1.2.3 Parallelization......Page 18
1.3 Optimization of Eigenvalues......Page 20
References......Page 28
2.1 Introduction......Page 30
2.2 Governing Equation......Page 32
2.3 BEM Formulation of Transient Convection-Diffusion-Reaction Problems......Page 33
2.4 Standard Approach: DRBEM......Page 34
2.5 Discretization......Page 36
2.6 Handling Convective Terms......Page 38
2.7 Time Marching Solution Scheme......Page 39
2.8 The Choice of Radial Basis Functions......Page 40
2.9.1 Transient Convection-Diffusion-Reaction over a Square Channel with Time-Dependent Dirichlet Boundary Conditions and Tangential Velocity Field......Page 42
2.9.2 Transient Convection-Diffusion-Reaction Problem over Rectangular Region with Mixed (Neumann–Dirichlet) Boundary Conditions......Page 47
References......Page 50
3.1 Introduction......Page 53
3.2 The Simulation......Page 54
3.3 Results......Page 59
3.4 Conclusion......Page 65
References......Page 66
4.1 Introduction......Page 68
4.2 Mathematical Formulation......Page 69
4.3.1 Discretization and Matrix System......Page 71
4.3.2 Numerical Integration......Page 72
4.3.3 Analytic Treatment of the Source Term......Page 73
4.4.1 Concentration Profiles for Various Peclet Numbers......Page 75
4.4.2 Mesh Size Sensitivity......Page 76
4.5 Applications with Point Sources......Page 78
References......Page 80
5.1 Introduction......Page 81
5.2 The Plate Equations......Page 82
5.3 Dirichlet Boundary Value Problem......Page 83
5.4 Generalized Fourier Series Method......Page 88
5.5 Computational Procedure......Page 91
5.6 Numerical and Graphical Illustration: Known Solution......Page 94
5.7 Numerical and Graphical Illustration: Unknown Solution......Page 102
References......Page 105
6.1 Introduction and Statement of the Problem......Page 107
6.2 Some Explicit Computations......Page 110
6.3 Asymptotic Expansions for Low Frequencies......Page 116
6.4 On Convergence for Low Frequencies......Page 123
6.5 High Frequencies......Page 129
References......Page 131
7.1 Introduction......Page 133
7.2 Setting of the Problem......Page 137
7.2.1 The Spectrum and the Estimates for Eigenvalues......Page 139
7.3 The Spectral Homogenized Problems......Page 140
7.4 Asymptotic Expansions......Page 143
7.4.1 The Stationary Local Problems......Page 144
7.4.2 The Boundary Condition on Σ......Page 145
7.5 Abstract Framework for Local and Homogenized Problems......Page 149
7.5.1 The Case of an Isotropic Medium......Page 150
7.5.2 Setting of the Homogenized Problems......Page 152
References......Page 154
8.1 Introduction......Page 157
8.2 Description of the Problem......Page 158
8.3.1 Description of the Model......Page 160
8.3.2 Numerical Results with the Simple Model......Page 162
8.4.1 Fluid Motion......Page 164
8.4.2 Spread of the Chemical Signal......Page 165
8.4.3 Time Integration......Page 167
8.5 Simplified Boundary Integral Model......Page 168
8.5.1 Numerical Results with the Boundary Integral Method......Page 172
8.6 Conclusions and Future Work......Page 174
References......Page 176
9.1 Introduction......Page 178
9.2 A Review on Some Theoretical Results......Page 180
9.3 System of Boundary Integral Equations and Its Approximation......Page 184
9.3.1 First Boundary Integral Equation......Page 185
9.3.3 Third Boundary Integral Equation......Page 186
9.3.4 Fourth Boundary Integral Equation......Page 187
9.3.5 System of Boundary Integral Equations......Page 188
9.4 Numerical Results......Page 189
9.5 Summary and Conclusion......Page 196
Appendix......Page 197
References......Page 198
10.1 Introduction......Page 201
10.2 Preliminaries and Notation......Page 204
10.3 Definition of Outer Nontangential Unit Vector Field and Introduction of a Neighborhood of the Boundary......Page 207
10.4 An Inequality for Hölder Continuous Functions on Local Hypographs......Page 211
Appendix......Page 221
References......Page 224
11.1 Introduction......Page 226
11.2 Physical and Mathematical Model......Page 227
11.3.1 Waterflooding......Page 228
11.3.2 Polymer Flooding......Page 231
11.3.3 Miscible Flooding......Page 235
References......Page 240
12.1 Introduction......Page 241
12.2 Alternative Dynamic Iteration Schemes and Their Distinct Convergence Properties......Page 243
12.3 Error Analysis......Page 246
12.4 Numerical Experiments and Illustrations......Page 249
12.5 Methods Comparison......Page 253
12.6 Concluding Remarks and Future Work......Page 257
References......Page 258
Index......Page 259