Ebook: 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.

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Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Asymptotics and Numerics for Laminar Flow Over a Finite Flat Plate....Pages 3-19
Time-Scale Decoupling for Nearly Periodic Advection-Diffusion Equations....Pages 21-39
Turbulence Modeling from an Asymptotic Point of View....Pages 41-52
Some Applications of Combined Asymptotics and Numerics in Fluid Mechanics and Aerodynamics....Pages 53-79
Asymptotic-Assisted Numerics for Spectral Perturbation in MHD Instability....Pages 81-90
Front Matter....Pages 91-91
Domain Decomposition as a Mechanism for Using Asymptotic Methods....Pages 93-105
Domain Decomposition: A Blowup Problem and the Ginzburg-Landau Equations....Pages 107-122
Factorization of the Advection-Diffusion Operator and Domain Decomposition Method....Pages 123-133
Front Matter....Pages 135-135
Modulated Traveling Waves in Combustion....Pages 137-162
Asymptotics and Multiscale Simulation in a Numerical Combustion Laboratory....Pages 163-187
Front Matter....Pages 189-189
Viscoelastic Fluid Flow: Critical Parameters and Asymptotics....Pages 191-205
Exponentially Small Splitting of Homoclinic Orbits in a Water-Wave Problem....Pages 207-214
Supersensitive Boundary Value Problems....Pages 215-223
Asymptotics of the Thual-Fauve Pulse....Pages 225-239
Exponential Convergence of the Galerkin Approximation for the Ginzburg-Landau Equation....Pages 241-252
Front Matter....Pages 253-253
General Asymptotic Scales and Computer Algebra....Pages 255-266
Front Matter....Pages 267-267
Domain Decomposition by the Mortar Element Method....Pages 269-286
Multilevel Projection Methods for Partial Differential Equations....Pages 287-292
A Parallel Adaptive Multigrid Algorithm for the Incompressible Navier-Stokes Equations....Pages 293-309
Numerical Approximation of a Two-Dimensional Singular-Perturbation Problem Using an Asymptotic Expansion and a Finite Element Method....Pages 311-319
Front Matter....Pages 267-267
Internal Boundary Conditions and the Feedback Loop for Nested Two-Way Communication Schemes....Pages 321-334
Subdomain Predictor-Corrector Algorithms for Solving the Incompressible Navier-Stokes Equation....Pages 335-347
Parallel Blas and Blacs for Numerical Algorithms on a Reconfigurable Network....Pages 349-366
Back Matter....Pages 367-372

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Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Asymptotics and Numerics for Laminar Flow Over a Finite Flat Plate....Pages 3-19
Time-Scale Decoupling for Nearly Periodic Advection-Diffusion Equations....Pages 21-39
Turbulence Modeling from an Asymptotic Point of View....Pages 41-52
Some Applications of Combined Asymptotics and Numerics in Fluid Mechanics and Aerodynamics....Pages 53-79
Asymptotic-Assisted Numerics for Spectral Perturbation in MHD Instability....Pages 81-90
Front Matter....Pages 91-91
Domain Decomposition as a Mechanism for Using Asymptotic Methods....Pages 93-105
Domain Decomposition: A Blowup Problem and the Ginzburg-Landau Equations....Pages 107-122
Factorization of the Advection-Diffusion Operator and Domain Decomposition Method....Pages 123-133
Front Matter....Pages 135-135
Modulated Traveling Waves in Combustion....Pages 137-162
Asymptotics and Multiscale Simulation in a Numerical Combustion Laboratory....Pages 163-187
Front Matter....Pages 189-189
Viscoelastic Fluid Flow: Critical Parameters and Asymptotics....Pages 191-205
Exponentially Small Splitting of Homoclinic Orbits in a Water-Wave Problem....Pages 207-214
Supersensitive Boundary Value Problems....Pages 215-223
Asymptotics of the Thual-Fauve Pulse....Pages 225-239
Exponential Convergence of the Galerkin Approximation for the Ginzburg-Landau Equation....Pages 241-252
Front Matter....Pages 253-253
General Asymptotic Scales and Computer Algebra....Pages 255-266
Front Matter....Pages 267-267
Domain Decomposition by the Mortar Element Method....Pages 269-286
Multilevel Projection Methods for Partial Differential Equations....Pages 287-292
A Parallel Adaptive Multigrid Algorithm for the Incompressible Navier-Stokes Equations....Pages 293-309
Numerical Approximation of a Two-Dimensional Singular-Perturbation Problem Using an Asymptotic Expansion and a Finite Element Method....Pages 311-319
Front Matter....Pages 267-267
Internal Boundary Conditions and the Feedback Loop for Nested Two-Way Communication Schemes....Pages 321-334
Subdomain Predictor-Corrector Algorithms for Solving the Incompressible Navier-Stokes Equation....Pages 335-347
Parallel Blas and Blacs for Numerical Algorithms on a Reconfigurable Network....Pages 349-366
Back Matter....Pages 367-372
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