Recent Advances in Numerical Methods for Partial Differential Equations and Applications
About this Title
Xiaobing Feng and Tim P. Schulze, Editors
An emerging field over the past 15 years, computational mathematics is a vast area which has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry.
Compiled here are six of nine in-depth survey papers with an expository discussion on computational mathematics that were presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. They focus on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Each of the lecturers is a leading researcher in the field of computational mathematics and its applications.
This book will be a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists. Prior knowledge of partial differential equations and their numerical methods is helpful.
Graduate students and research mathematicians interested in numerical methods for partial differential equations.
Table of Contents
- Jinchao Xu and Aihui Zhou – Some multiscale methods for partial differential equations [MR 1940621]
- David E. Keyes – Terascale implicit methods for partial differential equations [MR 1940622]
- Małgorzata Peszyńska, Eleanor W. Jenkins and Mary F. Wheeler – Boundary conditions for fully implicit two-phase flow models [MR 1940623]
- G. B. McFadden – Phase-field models of solidification [MR 1940624]
- Qing Nie, Saleh Tanveer, Todd F. Dupont and Xiaofan Li – Singularity formation in free-surface Stokes flows [MR 1940625]
- Craig C. Douglas and Dan T. Thorne – A note on cache memory methods for multigrid in three dimensions [MR 1940626]