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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| Veröffentlicht in: | SIAM journal on numerical analysis Jg. 34; H. 4; S. 1513 - 1544 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Philadelphia, PA
Society for Industrial and Applied Mathematics
01.08.1997
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| ISSN: | 0036-1429, 1095-7170 |
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| Abstract | 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. |
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| AbstractList | 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. 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 $\varepsilon$. On the subdomains, iterative solution techniques are used, which may vary from one subdomain to another. The global convergence rate depends on $\varepsilon$; it generally increases like some power of $(\log (\varepsilon ^{-1}))^{-1}$ as $\varepsilon \downarrow 0$. The method is illustrated on several two-dimensional singular perturbation problems. |
| Author | Kaper, Hans G. Garbey, Marc |
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| Copyright | Copyright 1997 Society for Industrial and Applied Mathematics 1997 INIST-CNRS [Copyright] © 1997 Society for Industrial and Applied Mathematics |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Heterogeneous Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems |
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