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 will gain 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. 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.

Inhalt

Wavelet-Based Multiresolution Methods for Stationary PDEs and PDE-Constrained Control Problems.- On Approximation in Meshless Methods.- Theory and Applications of Smoothed Particle Hydrodynamics.- Efficient Implementation and Parallelization of Meshfree and Particle Methods-The Parallel Multilevel Partition of Unity Method.