| Invited lectures | |
| Domain Decomposition Methods | p. 3 |
| Introduction | p. 3 |
| Iterative Methods and Preconditioners | p. 5 |
| Classical Alternating Schwarz Algorithms | p. 8 |
| Multidomain Schwarz Methods and Coarse Spaces | p. 13 |
| Additive Schwarz Methods | p. 15 |
| Hybrid Schwarz Methods | p. 15 |
| Abstract Schwarz Theory | p. 17 |
| Final Remarks | p. 24 |
| Modification and Maintenance of ULV Decompositions | p. 31 |
| Introduction | p. 31 |
| Matrix Computational Tools for the ULVD | p. 34 |
| Forming a ULVD | p. 38 |
| Modifying a ULVD | p. 44 |
| Refining a ULVD | p. 56 |
| Conclusion | p. 60 |
| Advances in Jacobi Methods | p. 63 |
| Two Sided Methods | p. 64 |
| Asymptotic Convergence | p. 71 |
| Accuracy | p. 78 |
| Modelling of curved rods | p. 91 |
| Introduction | p. 91 |
| Curved rod | p. 92 |
| Three-dimensional equations of linearized elasticity | p. 94 |
| Curvilinear coordinates | p. 97 |
| One-dimensional models of curved rods | p. 100 |
| The Korn inequality | p. 107 |
| A priori estimates, convergence | p. 108 |
| Differential form of curved rod model | p. 113 |
| Comparison of various curved rod models | p. 116 |
| Incompressible Newtonian flow through thin pipes | p. 123 |
| Introduction | p. 123 |
| Poiseuille approximation for pipe with variable cross-section | p. 125 |
| Justification of the Kirchoff's law | p. 129 |
| Curved pipes | p. 134 |
| Conclusion | p. 140 |
| First Order Eigenvalue Perturbation Theory and the Newton Diagram | p. 143 |
| Introduction | p. 143 |
| The Newton Diagram | p. 146 |
| First order perturbation bounds for eigenvalues | p. 149 |
| First order perturbation bounds for singular values | p. 168 |
| First order perturbation bounds for generalized eigenvalues | p. 171 |
| Contributed lectures | |
| Microlocal energy density for hyperbolic systems | p. 179 |
| Introduction | p. 179 |
| On H-measures | p. 180 |
| Main result | p. 183 |
| Another approach | p. 187 |
| Approximate solutions to some second order linear recurrences | p. 191 |
| Introduction | p. 191 |
| Riccati difference equation for the error term | p. 193 |
| A simple error estimation | p. 194 |
| Example | p. 195 |
| Asymptotic Behaviour of Tension Spline Collocation Matrix | p. 199 |
| Preliminaries | p. 200 |
| B-splines | p. 200 |
| Collocation method | p. 202 |
| Asymptotic behavior of the collocation matrix | p. 203 |
| Numerical stability of Krylov subspace iterative methods for solving linear systems | p. 209 |
| Introduction | p. 209 |
| Iterative methods that recursively compute residual | p. 210 |
| Methods that solve least squares problem | p. 213 |
| Conclusion | p. 216 |
| Nonlinear Problems in Dynamics by the Finite Element in Time Method | p. 219 |
| Introduction | p. 219 |
| Problem formulation | p. 220 |
| Finite element in time method | p. 221 |
| Stability analysis | p. 225 |
| Concluding remarks | p. 227 |
| On directional bias of the L[subscript p]-norm | p. 229 |
| Introduction | p. 229 |
| Directional bias of the L[subscript p]-norm on R[superscript 3] | p. 231 |
| Directional bias of the L[subscript p]-norm on R[superscript n] | p. 233 |
| A note on slip condition on corrugated boundary | p. 237 |
| Description of the geometry | p. 238 |
| The equations of motion | p. 239 |
| Some technical results | p. 240 |
| Existence, uniqueness, regularity and a priori estimates | p. 241 |
| The convergence | p. 244 |
| Relaxation of some energy functions related to the formation of microstructure | p. 251 |
| Introduction | p. 251 |
| Formulation of the problem | p. 252 |
| Some results | p. 254 |
| A Coarse Space for Elasticity | p. 261 |
| Introduction | p. 261 |
| Linear Elasticity Discretization | p. 262 |
| Algebraic Subregions | p. 263 |
| Overlapping Schwarz Methods | p. 264 |
| Theoretical Analysis | p. 267 |
| Numerical Approximations of the Sediment Transport Equations | p. 275 |
| Numerical treatment of the sediment transport equations | p. 277 |
| Numerical schemes | p. 277 |
| Exact C-property | p. 281 |
| Numerical results | p. 283 |
| Conclusion remarks | p. 286 |
| A model of irregular curved rods | p. 289 |
| Introduction | p. 289 |
| Curved rod model | p. 290 |
| Curved rod model of irregular rods | p. 292 |
| Error estimate | p. 295 |
| Comparison with the junction model | p. 297 |
| Perspectives | p. 298 |
| Existence of the density of states for some alloy type models with single site potentials that change sign | p. 301 |
| Alloy type model and the integrated density of states | p. 301 |
| Main theorem: A Wegner estimate for indefinite potentials | p. 303 |
| Sketch of the proof of Theorem 2.1 | p. 304 |
| Discussion and Applications | p. 305 |
| On principal eigenvalue of stationary diffusion problem with nonsymmetric coefficients | p. 313 |
| Homogenisation of eigenvalue problem | p. 315 |
| Optimal design for principal eigenvalue optimisation | p. 317 |
| Singular values | p. 319 |
| Qualitative Analysis of some Solutions of Quasilinear System of Differential Equations | p. 323 |
| Introduction | p. 323 |
| The main results | p. 324 |
| Applications | p. 330 |
| High-Order ENO and WENO Schemes with Flux Gradient and Source Term Balancing | p. 333 |
| Introduction | p. 333 |
| ENO and WENO Reconstruction via Primitive Function | p. 335 |
| LLF Formulations | p. 336 |
| RF Formulations | p. 338 |
| The One-dimensional Shallow Water Equations and the C-property | p. 339 |
| Test Problems | p. 341 |
| Concluding Remarks | p. 343 |
| Index | p. 347 |
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