Frontiers of Numerical Analysis: Durham 2004

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James Blowey, Alan Craig
Springer Science & Business Media, Mar 30, 2006 - Computers - 266 pages
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This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.
 

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Contents

Wavelet Methods for Stationary PDEs and PDEConstrained
1
Wavelets
13
Problems in Wavelet Coordinates
33
Iterative Solution
44
References
60
Polynomial Reproducing Systems
69
Partition of Unity Method and Generalized FEM
93
A Results from Analysis
122
Theory and Applications of Smoothed Particle Hydrodynamics143
142
Lagrangian SPH
167
SPH Heat Conduction
177
Viscosity
183
References
193
Efficient Implementation
212
Parallelization
243
References
258

References
136

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