Frontiers And Prospects of Contemporary Applied Mathematics (Series in Contemporary Applied Mathematics Cam)

This collection of articles covers the hottest topics in contemporary applied mathematics. Multiscale modeling, material computing, symplectic methods, parallel computing, mathematical biology, applied differential equations and engineering computing problems are all included. The book contains the latest results of many leading scientists and provides a window on new trends in research in the field. Sample Chapter(s). Chapter 1: An Iterative BEM for the Inverse Problem of Detecting Corrosion in a Pipe (467 KB). Contents: An Iterative BEM for the Inverse Problem of Detecting Corrosion in a Pip Contents......Page 6 Preface......Page 8 1 Introduction......Page 9 2 Formulation of the inverse problem......Page 10 3 The iterative boundary element method for this Cauchy problem......Page 12 4 Numerical results for the inverse problem......Page 21 References......Page 24 1 Introduction......Page 26 2 The existence theorem for the continuum and the atomistic models......Page 30 3 Local quasicontinuum method......Page 32 4 Estimate of e(QC)......Page 36 References......Page 39 1 Introduction......Page 41 2 Two typical problems......Page 43 3 The global (nonlocal) artificial boundary conditions......Page 45 4 Local boundary conditions......Page 50 5 Discrete artificial boundary conditions......Page 53 6 Implicit boundary conditions......Page 58 7 Conclusions......Page 59 References......Page 60 1 Introduction......Page 67 2 Extremal fundamental systems versus product rules......Page 68 3 Optimal order estimates for cubature in Sobolev spaces......Page 72 4 Numerical example......Page 76 References......Page 77 1 Introduction......Page 79 2 Multi-symplecticity of Runge-Kutta type methods for the general Hamiltonian partial differential equations......Page 85 3 Multi-symplectic Runge-Kutta type methods for Schrodinger equations......Page 95 4 Multi-symplectic Runge-Kutta methods for one dimensional Dirac equations......Page 105 5 Conclusions......Page 117 References......Page 118 1 Introduction......Page 122 2 Radiative transfer equation and diffusion approximation......Page 123 4 Bioluminescent tomography (BLT)......Page 128 5 Reformulation of BLT......Page 130 6 Uniqueness of BLT......Page 132 7 Uniqueness results for radial sources......Page 136 8 Reconstruction methods......Page 139 9 Discussions......Page 149 References......Page 150 1 Introduction......Page 157 2 The cell cycle network in yeast......Page 158 3 Model and simulation of the cell cycle network......Page 160 4 Comparison with random networks......Page 163 6 Conclusion......Page 165 References......Page 167 1 Introduction......Page 168 2 Model problem and finite element discretization......Page 170 3 AMG algorithm on uniform mesh......Page 172 4 Modified AMG algorithm and implementation......Page 180 5 Conclusion......Page 183 References......Page 184 1 Introduction......Page 187 2 Progress in two dimensions......Page 188 3 Progress in three dimensions......Page 194 References......Page 195 1 Introduction......Page 199 2 Lp-Lq decay estimates in linear thermoelastic system with second sound in 1-d......Page 200 3 Lp-Lq decay estimates in linear thermoelastic system with second sound in 3-d......Page 205 4 Asymptotic behaviour of discontinuities in thermoelasticity......Page 210 References......Page 214 1 Introduction......Page 216 2 Complete distance matrix and semidefinite matrix......Page 219 3 Complexity and uniqueness of configuration......Page 223 4 Algorithm based on coordinates......Page 228 References......Page 232 1 Introduction......Page 235 2 Equivalent integral equations......Page 237 3 Regularization solution......Page 239 4 Integral equation method for inversion......Page 241 5 Numerical performance......Page 245 References......Page 248 1 Introduction......Page 250 2 The mathematical model and numerical method......Page 251 3 Parallel arithmetic and parallel program......Page 254 4 Validity analysis of parallel arithmetic......Page 255 5 Numerical analysis of the model problem......Page 258 References......Page 260 1 Introduction......Page 262 2 Strong tractability in worst-case setting......Page 265 3 Tractability in random-case setting......Page 272 References......Page 274 2 Multi-symplecticity of Runge-Kutta type methods for the general Hamiltonian partial differential equations3 Multi-symplectic Runge-Kutta type methods for Schrodinger equations; 4 Multi-symplectic Runge-Kutta methods for one dimensional Dirac equations; 5 Conclusions; References; Inverse Problems in Bioluminescence Tomography; 1 Introduction; 2 Radiative transfer equation and diffusion approximation; 3 Optical tomography; 4 Bioluminescent tomography (BLT); 5 Reformulation of BLT; 6 Uniqueness of BLT; 7 Uniqueness results for radial sources; 8 Reconstruction methods; 9 Discussions; References Global Dynamic Properties of Protein Networks1 Introduction; 2 The cell cycle network in yeast; 3 Model and simulation of the cell cycle network; 4 Comparison with random networks; 5 The life cycle network; 6 Conclusion; References; A Modified Adaptive Algebraic Multigrid Algorithm for Elliptic Obstacle Problems; 1 Introduction; 2 Model problem and finite element discretization; 3 AMG algorithm on uniform mesh; 4 Modified AMG algorithm and implementation; 5 Conclusion; References; Parallel Algorithms and Implementation Techniques for Terascale Numerical Simulations of Typical Applications 1 Introduction2 Progress in two dimensions; 3 Progress in three dimensions; 4 Related works; References; Long Time Behaviour of Solutions to Linear Thermoelastic Systems with Second Sound; 1 Introduction; 2 Lp-Lq decay estimates in linear thermoelastic system with second sound in 1-d; 3 Lp-Lq decay estimates in linear thermoelastic system with second sound in 3-d; 4 Asymptotic behaviour of discontinuities in thermoelasticity; References; Contributed Talks; Distance Geometry Problem and Algorithm Based on Barycentric Coordinates; 1 Introduction 1 Introduction2 Two typical problems; 3 The global (nonlocal) artificial boundary conditions; 4 Local boundary conditions; 5 Discrete artificial boundary conditions; 6 Implicit boundary conditions; 7 Conclusions; References; Optimal order integration on the sphere; 1 Introduction; 2 Extremal fundamental systems versus product rules; 3 Optimal order estimates for cubature in Sobolev spaces; 4 Numerical example; References; A Survey of Multi-symplectic Runge-Kutta Type Methods for Hamiltonian Partial Differential Equations; 1 Introduction