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Recent Advances in Numerical Methods for Partial Differential Equations and Applications
Edited by: Xiaobing Feng, University of Tennessee, Knoxville, TN, and Tim P. Schulze, New York University-Courant Institute, NY

Contemporary Mathematics
2002; 177 pp; softcover
Volume: 306
ISBN-10: 0-8218-2970-X
ISBN-13: 978-0-8218-2970-7
List Price: US$60
Member Price: US$48
Order Code: CONM/306
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This book is derived from lectures presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. The topic was computational mathematics, focusing on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Compiled here are articles from six of nine speakers. Each of them is a leading researcher in the field of computational mathematics and its applications.

A vast area that has been coming into its own over the past 15 years, computational mathematics 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. With the aid of powerful high performance computers, numerical simulation of physical phenomena is the only feasible method for analyzing many types of important phenomena, joining experimentation and theoretical analysis as the third method of scientific investigation.

The three aspects: applications, theory, and computer implementation comprise a comprehensive overview of the topic. Leading lecturers were Mary Wheeler on applications, Jinchao Xu on theory, and David Keyes on computer implementation.

Following the tradition of the Barrett Lectures, these in-depth articles and expository discussions make this book a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists.


Graduate students and research mathematicians interested in numerical methods for partial differential equations.

Table of Contents

  • J. Xu and A. Zhou -- Some multiscale methods for partial differential equations
  • D. E. Keyes -- Terascale implicit methods for partial differential equations
  • M. Peszyńska, E. W. Jenkins, and M. F. Wheeler -- Boundary conditions for fully implicit two-phase flow models
  • G. B. McFadden -- Phase-field models of solidification
  • Q. Nie, S. Tanveer, T. F. Dupont, and X. Li -- Singularity formation in free-surface Stokes flows
  • C. C. Douglas and D. T. Thorne -- A note on cache memory methods for multigrid in three dimensions
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