Absorbing boundary conditions for domain decomposition
1998 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 27, no 4, 341-365 p.Article in journal (Refereed) Published
In this paper we would like to point out some similarities between two artificial boundary conditions. One is the far field or absorbing boundary conditions for computations over unbounded domain. The other is the boundary conditions used at the boundary between subdomains in domain decomposition. We show some convergence result for the generalized Schwarz alternating method (GSAM), in which a convex combination of Dirichlet data and Neumann data is exchanged at the artificial boundary. We can see clearly how the mixed boundary condition and the relative size of overlap will affect the convergence rate. These results can be extended to more general coercive elliptic partial differential equations using the equivalence of elliptic operators. Numerically first- and second-order approximations of the Dirichlet-to-Neumann operator are constructed using local operators, where information tangential to the boundary is included. Some other possible extensions and applications are pointed out. Finally numerical results are presented.
Place, publisher, year, edition, pages
1998. Vol. 27, no 4, 341-365 p.
Partial differential equation (PDE); Domain decomposition; Schwarz alternating method (SAM); Absorbing boundary condition; Dirichlet-to-Neumann (DtN) operator; Immersed interface problem; Trace theorem
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-90362OAI: oai:DiVA.org:kth-90362DiVA: diva2:505029
NR 201408052012-02-222012-02-22Bibliographically approved