Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters

This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ­ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp­ totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na­ tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ­ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.

1: Modeling of Complex Systems with Asymptotic-enhanced Numerical Methods.- Asymptotics and Numerics for Laminar Flow over a Finite Flat Plate.- Time-Scale Decoupling for Nearly Periodic Advection-Diffusion Equations.- Turbulence Modeling from an Asymptotic Point of View.- Some Applications of Combined Asymptotics and Numerics in Fluid Mechanics and Aerodynamics.- Asymptotic-Assisted Numerics for Spectral Perturbation in MHD Instability.- 2: Asymptotic-induced Domain Decomposition Methods.- Domain Decomposition as a Mechanism for Using Asymptotic Methods.- Domain Decomposition: A Blowup Problem and the Ginzburg-Landau Equations.- Factorization of the Advection-Diffusion Operator and Domain Decomposition Method.- 3: Multiple-Scale Problems in Scientific Computing.- Modulated Traveling Waves in Combustion.- Asymptotics and Multiscale Simulation in a Numerical Combustion Laboratory.- 4: Applied and Asymptotic Analysis.- Viscoelastic Fluid Flow: Critical Parameters and Asymptotics.- Exponentially Small Splitting of Homoclinic Orbits in a Water-Wave Problem.- Supersensitive Boundary Value Problems.- Asymptotics of the Thual-Fauve Pulse.- Exponential Convergence of the Galerkin Approximation of the Ginzburg-Landau Equation.- 5: Symbolic Manipulation Tools for Asymptotic Analysis.- General Asymptotic Scales and Computer Algebra.- 6: Numerical Methods, Algorithms, and Architectures.- Domain Decomposition by the Mortar Element Method.- Multilevel Projection Methods for Partial Differential Equations.- A Parallel Adaptive Multigrid Algorithm for the Incompressible Navier-Stokes Equations.- Numerical Approximation of a 2-D Singular-Perturbation Problem Using an Asymptotic Expansion and a Finite Element Method.- Internal Boundary Conditions and the Feedback Loop for Nested Two-WayCommunication Schemes.- Subdomain Predictor-Corrector Algorithms for Solving the Incompressible Navier-Stokes Equation.- Parallel BLAS and BLACS for Numerical Algorithms on a Reconfigurable Network.