Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems

Technical Report · Fri Apr 14 04:00:00 EDT 1995

DOI:https://doi.org/10.2172/510563· OSTI ID:510563

Garbey, M ^[1]; Kaper, H G ^[2]

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1. Universite Claude Bernard Lyon, Villeurbanne (France)
2. Argonne National Lab., IL (United States)

A heterogeneous domain-decomposition method is presented for the numerical solution of singularly perturbed elliptic boundary value problem. The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The sub-domains match the domains of validity of the local ({open_quotes}inner{close_quotes} and {open_quotes}outer{close_quotes}) 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, {epsilon}. On the subdomains, iterative solution techniques are used, which may vary from one subdomain to another. The global convergence rate depends on {epsilon}; it generally increases like some power of (log({epsilon}{sup -1})){sup -1} as {epsilon} {down_arrow} 0. The method is illustrated on several two-dimensional singular perturbation problems.

• Research Organization: Argonne National Lab., IL (United States)
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States); Fondation Cromey-le-Bas
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 510563
• Report Number(s): MCS-P--510-0495; ON: DE97008371
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ASYMPTOTIC SOLUTIONS
BOUNDARY LAYERS
BOUNDARY-VALUE PROBLEMS
DISTURBANCES
ITERATIVE METHODS
PARTIAL DIFFERENTIAL EQUATIONS