Asymptotic and Numerical Methods for Partial Differential Equations With Critical Parameters

by Kaper, Hans G.; Garbey, Marc; Pieper, Gail W.

• ISBN13: 9780792320616
• ISBN10: 0792320611
• Format: Hardcover
• Copyright: 1993-01-01
• Publisher: Kluwer Academic Pub

Summary

This volume provides a record of the workshop on asymptotic-induced numerical methods for partial differential equations, critical parameters and domain decomposition, held at Beaune, France. Discussing new computational methods, recent algorithm developments, and state-of-the-art techniques in mathematical modeling, Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters explores important topics in theory and application, including: modeling of complex fluid dynamics systems; asymptotic-induced domain decomposition methods; analysis of strongly nonlinear problems; tools available for modern numerical analysis; and symbolic manipulation tools for multiscale problems. Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters presents a panoramic view of areas where asymptotic analysis, numerical analysis, and scientific computing are beginning to be integrated effectively. With articles ranging from mathematical models and applications to state-of-the-art algorithms and computational methods, the book is an invaluable text for mathematicians, engineers, and computer scientists who wish to become involved in this challenging new area of research.

Table of Contents

Preface
Contributors
Modeling of Complex Systems with Asymptotic-enhanced Numerical Methods	p. 1
Asymptotics and Numerics for Laminar Flow over a Finite Flat Plate	p. 3
Time-Scale Decoupling for Nearly Periodic Advection-Diffusion Equations	p. 21
Turbulence Modeling from an Asymptotic Point of View	p. 41
Some Applications of Combined Asymptotics and Numerics in Fluid Mechanics and Aerodynamics	p. 53
Asymptotic-Assisted Numerics for Spectral Perturbation in MHD Instability	p. 81
Asymptotic-induced Domain Decomposition Methods	p. 91
Domain Decomposition as a Mechanism for Using Asymptotic Methods	p. 93
Domain Decomposition: A Blowup Problem and the Ginzburg-Landau Equations	p. 107
Factorization of the Advection-Diffusion Operator and Domain Decomposition Method	p. 123
Multiple-Scale Problems in Scientific Computing	p. 135
Modulated Traveling Waves in Combustion	p. 137
Asymptotics and Multiscale Simulation in a Numerical Combustion Laboratory	p. 163
Applied and Asymptotic Analysis	p. 189
Viscoelastic Fluid Flow: Critical Parameters and Asymptotics	p. 191
Exponentially Small Splitting of Homoclinic Orbits in a Water-Wave Problem	p. 207
Supersensitive Boundary Value Problems	p. 215
Asymptotics of the Thual-Fauve Pulse	p. 225
Exponential Convergence of the Galerkin Approximation of the Ginzburg-Landau Equation	p. 241
Symbolic Manipulation Tools for Asymptotic Analysis	p. 253
General Asymptotic Scales and Computer Algebra	p. 255
Numerical Methods, Algorithms, and Architectures	p. 267
Domain Decomposition by the Mortar Element Method	p. 269
Multilevel Projection Methods for Partial Differential Equations	p. 287
A Parallel Adaptive Multigrid Algorithm for the Incompressible Navier-Stokes Equations	p. 293
Numerical Approximation of a 2-D Singular-Perturbation Problem Using an Asymptotic Expansion and a Finite Element Method	p. 311
Internal Boundary Conditions and the Feedback Loop for Nested Two-Way Communication Schemes	p. 321
Subdomain Predictor-Corrector Algorithms for Solving the Incompressible Navier-Stokes Equation	p. 335
Parallel BLAS and BLACS for Numerical Algorithms on a Reconfigurable Network	p. 349
Index	p. 367
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