Recent Advances in Computational Sciences: Selected Papers from the International Workshop on Computational Sciences and Its Education; Beijing, China 29-31 August 2005

CONTENTS......Page 10
Preface......Page 6
1. Introduction......Page 14
2. GRP Scheme - Basic Properties......Page 16
3. Self-Similar Solutions in 2-D......Page 19
4. The Analysis of 2-D Riemann-Type Solutions......Page 20
5. The 2-D Guckenheimer Equation......Page 23
6. Euler Equations of Quasi I-D Compressible Inviscid Flow......Page 28
7. The GRP for Quasi l-D Compressible Inviscid Flow......Page 31
8. The GRP Numerical Method for Quasi I-D Compressible Inviscid Flow......Page 40
9. Fluid Dynamical Examples......Page 46
9.1. Wave Dynamics in a Duct with a Converging Segment......Page 47
9.2. Shock diffraction by a square cavity......Page 53
9.3. Second reflection of a shock wave by a double wedge......Page 55
9.4. Lagrange-Euler Scheme for a Gas-Grains Mixture......Page 57
References......Page 60
1. Introduction......Page 63
2. Formulations......Page 64
2.1. Model problem......Page 65
2.2. Remarks......Page 66
3. Base functions under variables separated condition......Page 67
4.1. Implementation and explanation......Page 68
4.2. Experiment results......Page 69
References......Page 76
1. Introduction......Page 78
2.1. Governing equations......Page 79
2.3. Dimensionless form......Page 80
3.1. Arbitrary Lagrangian Eulerian (ALE) Approach......Page 81
3.2. Variational form......Page 82
3.5. Solving the discrete problems......Page 83
3.7. Automatic mesh moving techniques......Page 84
4. Numerical results......Page 85
References......Page 90
1. Introduction......Page 93
3.1. A computational domain representation......Page 95
3.2. A physical domain representation......Page 97
3.3. Fourier-Spectral Implementation of MMPDEs......Page 98
3.4. Comparisons of two representations......Page 100
4.1. Allen-Cahn equations......Page 102
4.2. Numerical examples for Allen- Cahn equations......Page 103
5.1. Extension to Cahn-Hilliard equation......Page 104
5.2. Extension to Phase Field Inhomogeneous Elasticity Equations......Page 105
5.3. Switching on the Mesh Adaptation......Page 107
5.4. Further discussion......Page 109
References......Page 110
1. Introduction......Page 113
2. Finite volume evolution Galerkin methods......Page 115
3. Discontinuous Galerkin methods......Page 116
4.1. Shallow Water Equations......Page 118
4.2. Dam break problem......Page 120
4.3. Accuracy and efficiency tests......Page 121
5. Conclusion......Page 122
References......Page 123
1. Introduction......Page 129
2. Maxwell's equations and dispersive media......Page 130
3.1. Standard error analysis......Page 132
3.2. Superconvergence analysis......Page 134
4.2. Hp-adaptive methods......Page 136
4.3. A posteriori error estimation......Page 137
References......Page 138
1. Introduction......Page 146
2. Finite element approximation of boundary control problems......Page 147
3. Superconvergence analysis and recovery for the control u......Page 151
4. Superconvergence analysis for state and co-state and recovery type a posteriori error estimates......Page 156
5. Numerical examples......Page 163
References......Page 167
1. Introduction......Page 169
2.1. Preliminaries......Page 171
2.2. Optimal Quadratic Spline Collocation Methods......Page 172
2.3. Numerical Results......Page 177
3. Helmholtz Problem......Page 178
3.1. New Optimal Quadratic Spline Collocation Method......Page 180
3.2. Numerical Results......Page 183
4. Extensions and Generalizations......Page 184
Acknowledgment......Page 185
References......Page 186
1. Introdution......Page 188
2.1. The Eigenvalue Error Expansion for The First Type of Eigenvalue Problems......Page 189
2.2. The Eigenvalue Error Expansion for The Second Type of Eigenvalue Problems......Page 191
3. Mixed FEMs for Second Order Elliptic Eigenvalue Problems......Page 192
3.1. Two Dimensional Rectangular RTo Element......Page 193
3.2. Two Dimensional Rectangular RTk Element......Page 195
3.3. Two Dimensional Rectangular BDF Mk Element......Page 196
3.4. Three Dimensional RTo Element......Page 197
4. Mixed FEMs for Biharmonic Eigenvalue Problems......Page 198
4.1. Q1 Element......Page 199
5. Mixed FEMs for Stokes Eigenvalue Problems......Page 200
5.1. B - R Rectangular Element......Page 201
5.2. Q2 - P 1 Rectangular Element......Page 202
5.3. Hood-Taylor Rectangular Element......Page 203
5.4. Q1 - Qo Rectangular Element......Page 205
5.5. Hood-Taylor Triangular Element......Page 206
5.6. PI - PI Triangular Element......Page 208
5.7. Another Form for Stokes Problems......Page 210
References......Page 211
1. Green Function Iterations......Page 214
2. Background Material......Page 216
3. Proof of Main Result......Page 218
4. Concluding Remarks......Page 219
References......Page 220
1. Introduction......Page 222
2.1. General Notation......Page 224
2.2. Preliminary Lemmas......Page 225
2.3. Lemmas on Convolution......Page 226
3. Amalgam Spaces and Convolution on the Affine Group......Page 227
References......Page 230
1. Introduction......Page 231
2. A new frame approximation operator (IT;{ ('))1n......Page 233
3. Approximation by (0":;[ ('»rrt......Page 235
References......Page 240
1. Introduction......Page 241
2.1. Sampling functions associated with scaling functions......Page 244
2.2. Sampling and hybrid sampling series in scaling spaces......Page 246
3. The Gibbs phenomenon in hybrid sampling series......Page 248
3.1. Abel mean for wavelet with compact support......Page 249
3.2. The positive hybrid sampling series......Page 250
4. Numerical examples......Page 251
References......Page 253
1. Introduction and Related Work......Page 256
2. Segmentation Guided Registration Model......Page 258
2.1. Frameworks based on intensity homegeneity......Page 260
2.2. Level Set Formulation of the LC-based model......Page 261
3.1. Registration based on the Segmentation + Registration Component......Page 262
3.2. Registrations of our Segmentation + Registration LC model......Page 264
References......Page 265
1. Introduction......Page 268
2. Geometric Hermite interpolation with a PH cubic......Page 269
3. Examples......Page 272
References......Page 273
1. Introduction......Page 274
2. Formulation of the problem......Page 275
3. The Velocity Method......Page 276
4. A Saddle Point Formulation......Page 277
5. Function Space Parametrization......Page 279
6. Function Space Embedding......Page 287
Acknowledgments......Page 289
References......Page 290
1. Introduction......Page 291
2. Mathematical Formulation......Page 293
3. Numerical Algorithm......Page 296
4. Validation of Numerical Algorithm......Page 297
5. Results and Discussion......Page 300
5.1. Streamlines patterns depending on the Reynolds number and rate of rotation......Page 302
5.2. Streamline patterns depending on the gap spacing and the rate of rotation......Page 304
6. Conclusion......Page 306
References......Page 307
1. Introduction......Page 310
2. Main results......Page 311
3. Examples......Page 313
References......Page 315
1. Introduction......Page 317
2.1. Properties of the SDLS problem......Page 320
2.2. Algorithm Description......Page 321
2.3. Numerical approaches for solving the iteration equation......Page 322
2.3.2. Solution of B2Bli B! 8), = B2Bl i f - r......Page 324
3. Experiments......Page 325
Appendix A. Algorithm for Data Least Squares......Page 326
References......Page 328
1. Introduction......Page 331
2. Bisections in adaptive finite element methods......Page 332
2.1. Newest vertex bisection......Page 333
3.1. Data structure......Page 334
3.2. Initial labeling......Page 335
3.3. Marking strategy......Page 337
4. Numerical example......Page 340
Appendix A: Matlab code for bisection......Page 343
References......Page 344
1. INTRODUCTION......Page 346
2. IMPROVED ITERATION OF REGULARIZATION......Page 348
3. NUMERICAL RESULTS......Page 351
4. CONCLUSIONS AND FURTHER WORK......Page 352
References......Page 358
1. Spirit......Page 359
2. Content......Page 360
3. Web......Page 361
Four Special Matrices......Page 362
References......Page 369
1.1. Height Measurement for Short Curve......Page 370
1.2. Height Measurement for Long Curve......Page 372
1.4. Explicit Error......Page 373
3. Better Accuracy and TT......Page 374
4. Good Accuracy and Quadrature Rules......Page 375
5. Direct Proof of B-H-X Theorem......Page 376
6. Explaining All of Calculus in a Single Figure......Page 377
7. Generalization to Two Dimensions......Page 378
8. Generalization to Abstract Functions......Page 379
9. Appendix......Page 380
References......Page 382
1. Interaction between technology, research in mathematics, and teaching......Page 384
2.1. Multiresolutions......Page 386
2.2. Fractals......Page 388
2.3. Data mining......Page 389
3.1. Technology impacts the form and manner of teaching......Page 390
Acknowledgments.......Page 391
References......Page 392
Author Index......Page 394