Heterogeneous Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems

A heterogeneous domain-decomposition method is presented for the numerical solution of singularly perturbed elliptic boundary value problems. The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The subdomains match the domains of validity of the local (i...

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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 34; no. 4; pp. 1513 - 1544
Main Authors: Garbey, Marc, Kaper, Hans G.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.08.1997
Subjects:
Approximation
Boundary layers
Boundary value problems
Coordinate systems
Decomposition
Decomposition methods
Exact sciences and technology
Mathematical analysis
Mathematical functions
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Perceptron convergence procedure
Sciences and techniques of general use
Signal amplification
Transition layers
Truncation errors
Transition layer
Heterogeneous domain
Singular perturbation
Asymptotic behavior
Iterative method
Perturbed problem
Truncation error
Turning point problem
Convection equation
Elliptic equation
Boundary value problem
Discretization
Numerical solution
Convergence rate
Numerical simulation
Domain decomposition
Boundary layer
ISSN:0036-1429, 1095-7170
Online Access:Get full text
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Summary:A heterogeneous domain-decomposition method is presented for the numerical solution of singularly perturbed elliptic boundary value problems. The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The subdomains match the domains of validity of the local (inner and outer) asymptotic expansions, and cut-off functions are used to match solutions in neighboring subdomains. The positions of the interfaces, as well as the mesh widths, depend on the small parameter ε. On the subdomains, iterative solution techniques are used, which may vary from one subdomain to another. The global convergence rate depends on ε; it generally increases like some power of (log(ε-1))-1as$\varepsilon \downarrow 0$. The method is illustrated on several two-dimensional singular perturbation problems.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142995285587