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Applied Mathematics and Scientific Computing - Zlatko Drmac

Applied Mathematics and Scientific Computing

By: Zlatko Drmac (Editor), Vjeran Hari (Editor), Luka Sopta (Editor), Zvonimir Tutek (Editor), Kresimir Veselic (Editor)

Hardcover Published: 31st January 2003
ISBN: 9780306474262
Number Of Pages: 350

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Proceedings of the second conference on Applied Mathematics and Scientific Computing, held June 4-9, 2001 in Dubrovnik, Croatia.

The main idea of the conference was to bring together applied mathematicians both from outside academia, as well as experts from other areas (engineering, applied sciences) whose work involves advanced mathematical techniques.

During the meeting there were one complete mini-course, invited presentations, contributed talks and software presentations. A mini-course Schwarz Methods for Partial Differential Equations was given by Prof Marcus Sarkis (Worcester Polytechnic Institute, USA), and invited presentations were given by active researchers from the fields of numerical linear algebra, computational fluid dynamics, matrix theory and mathematical physics (fluid mechanics and elasticity).

This volume contains the mini-course and review papers by invited speakers (Part I), as well as selected contributed presentations from the field of analysis, numerical mathematics, and engineering applications.

Invited lectures
Domain Decomposition Methodsp. 3
Introductionp. 3
Iterative Methods and Preconditionersp. 5
Classical Alternating Schwarz Algorithmsp. 8
Multidomain Schwarz Methods and Coarse Spacesp. 13
Additive Schwarz Methodsp. 15
Hybrid Schwarz Methodsp. 15
Abstract Schwarz Theoryp. 17
Final Remarksp. 24
Modification and Maintenance of ULV Decompositionsp. 31
Introductionp. 31
Matrix Computational Tools for the ULVDp. 34
Forming a ULVDp. 38
Modifying a ULVDp. 44
Refining a ULVDp. 56
Conclusionp. 60
Advances in Jacobi Methodsp. 63
Two Sided Methodsp. 64
Asymptotic Convergencep. 71
Accuracyp. 78
Modelling of curved rodsp. 91
Introductionp. 91
Curved rodp. 92
Three-dimensional equations of linearized elasticityp. 94
Curvilinear coordinatesp. 97
One-dimensional models of curved rodsp. 100
The Korn inequalityp. 107
A priori estimates, convergencep. 108
Differential form of curved rod modelp. 113
Comparison of various curved rod modelsp. 116
Incompressible Newtonian flow through thin pipesp. 123
Introductionp. 123
Poiseuille approximation for pipe with variable cross-sectionp. 125
Justification of the Kirchoff's lawp. 129
Curved pipesp. 134
Conclusionp. 140
First Order Eigenvalue Perturbation Theory and the Newton Diagramp. 143
Introductionp. 143
The Newton Diagramp. 146
First order perturbation bounds for eigenvaluesp. 149
First order perturbation bounds for singular valuesp. 168
First order perturbation bounds for generalized eigenvaluesp. 171
Contributed lectures
Microlocal energy density for hyperbolic systemsp. 179
Introductionp. 179
On H-measuresp. 180
Main resultp. 183
Another approachp. 187
Approximate solutions to some second order linear recurrencesp. 191
Introductionp. 191
Riccati difference equation for the error termp. 193
A simple error estimationp. 194
Examplep. 195
Asymptotic Behaviour of Tension Spline Collocation Matrixp. 199
Preliminariesp. 200
B-splinesp. 200
Collocation methodp. 202
Asymptotic behavior of the collocation matrixp. 203
Numerical stability of Krylov subspace iterative methods for solving linear systemsp. 209
Introductionp. 209
Iterative methods that recursively compute residualp. 210
Methods that solve least squares problemp. 213
Conclusionp. 216
Nonlinear Problems in Dynamics by the Finite Element in Time Methodp. 219
Introductionp. 219
Problem formulationp. 220
Finite element in time methodp. 221
Stability analysisp. 225
Concluding remarksp. 227
On directional bias of the L[subscript p]-normp. 229
Introductionp. 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 boundaryp. 237
Description of the geometryp. 238
The equations of motionp. 239
Some technical resultsp. 240
Existence, uniqueness, regularity and a priori estimatesp. 241
The convergencep. 244
Relaxation of some energy functions related to the formation of microstructurep. 251
Introductionp. 251
Formulation of the problemp. 252
Some resultsp. 254
A Coarse Space for Elasticityp. 261
Introductionp. 261
Linear Elasticity Discretizationp. 262
Algebraic Subregionsp. 263
Overlapping Schwarz Methodsp. 264
Theoretical Analysisp. 267
Numerical Approximations of the Sediment Transport Equationsp. 275
Numerical treatment of the sediment transport equationsp. 277
Numerical schemesp. 277
Exact C-propertyp. 281
Numerical resultsp. 283
Conclusion remarksp. 286
A model of irregular curved rodsp. 289
Introductionp. 289
Curved rod modelp. 290
Curved rod model of irregular rodsp. 292
Error estimatep. 295
Comparison with the junction modelp. 297
Perspectivesp. 298
Existence of the density of states for some alloy type models with single site potentials that change signp. 301
Alloy type model and the integrated density of statesp. 301
Main theorem: A Wegner estimate for indefinite potentialsp. 303
Sketch of the proof of Theorem 2.1p. 304
Discussion and Applicationsp. 305
On principal eigenvalue of stationary diffusion problem with nonsymmetric coefficientsp. 313
Homogenisation of eigenvalue problemp. 315
Optimal design for principal eigenvalue optimisationp. 317
Singular valuesp. 319
Qualitative Analysis of some Solutions of Quasilinear System of Differential Equationsp. 323
Introductionp. 323
The main resultsp. 324
Applicationsp. 330
High-Order ENO and WENO Schemes with Flux Gradient and Source Term Balancingp. 333
Introductionp. 333
ENO and WENO Reconstruction via Primitive Functionp. 335
LLF Formulationsp. 336
RF Formulationsp. 338
The One-dimensional Shallow Water Equations and the C-propertyp. 339
Test Problemsp. 341
Concluding Remarksp. 343
Indexp. 347
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780306474262
ISBN-10: 0306474263
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 350
Published: 31st January 2003
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 24.23 x 18.64  x 2.9
Weight (kg): 0.88

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