Absorbing boundary conditions for domain decomposition

Applied Numerical Mathematics

Volumn 27, Issue 4, 1998, Pages 341-365

  Engquist, Bjorn ^a   Zhao, Hong Kai ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Absorbing boundary condition; Dirichlet to Neumann (DtN) operator; Domain decomposition; Immersed interface problem; Partial differential equation (PDE); Schwarz alternating method (SAM); Trace theorem

Indexed keywords

BOUNDARY CONDITIONS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; THEOREM PROVING;

ABSORBING BOUNDARY CONDITIONS; DIRICHLET-TO-NEUMANN OPERATOR; DOMAIN DECOMPOSITION; SCHWARZ ALTERNATING METHOD;

BOUNDARY VALUE PROBLEMS;

EID: 0032136457     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00019-1     Document Type: Article

References (24)

1. P. Bjørstad and O. Widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures, SIAM Numer. Anal. 23 (1986) 1097-1120.
2. T. Chan and T. Hou, Eigendecompositions of domain decomposition interface operators for constant coefficient elliptic problems, SIAM J. Sci. Comput. 12 (1991) 1471-1479.
3. Q. Dinh, R. Glowinski and J. Pénaux, Solving elliptic problems by domain decomposition methods with applications, in: Elliptic Problem Solvers II (Academic Press, New York, 1982).
4. M. Dryja and O.B. Widlund, Domain decomposition algorithms with small overlap, SIAM J. Sci. Comput. 15 (1994) 604-620.
5. H. Elman and G. Golub, Inexact and preconditioned Uzawa algorithms for saddle point problems, SIAM J. Numer. Anal. 31 (1994) 1645-1661.
6. B. Engquist and A. Majda, Absorbing boundary condition for the numerical simulation of waves, Math. Comp. 31 (1977) 629-651.
7. V. Faber, T. Manteuffel and S. Parter, On the equivalence of operators and the implications to preconditioned iterative methods for elliptic problems, Adv. Appl. Math. 11 (1989) 109-163.
8. T. Hou, Z. Li, S. Osher and H. Zhao, A hybrid method for moving interface problem with application to Hele - Shaw flow, J. Comput. Phys., to appear.
9. C. Johnson and C. Nedelec, On the coupling of boundary integral and finite element methods, Math. Comp. 35 (1980) 1063-1079.
10. J.B. Keller and D. Givoli, Exact non-reflecting boundary conditions, J. Comput. Phys. (1989) 172-192.
11. R. LeVeque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994) 1019-1044.
12. Z. Li, Immersed interface method for moving interface problems, Numer. Algorithms, to appear.
13. P. Lions, On the Schwarz alternating method I, in: T.F. Chan, R. Glowinski, J. Périaux and O. Widlund, eds., Proceedings of First International Symposium on Domain Decomposition Methods for Partial Differential Equations (SIAM, Philadelphia, PA, 1988) 1-42.
14. P. Lions, On the Schwarz alternating method II: Stochastic interpretation and order properties, in: T.F. Chan, R. Glowinski, J. Périaux and O. Widlund, eds., Proceedings of Second International Symposium on Domain Decomposition Methods for Partial Differential Equations (SIAM, Philadelphia, PA, 1989) 47-70.
15. P. Lions, On the Schwarz alternating method III: A variant for non-overlapping subdomains, in: T.F. Chan, R. Glowinski, J. Périaux and O. Widlund, eds., Proceedings of Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (SIAM, Philadelphia, PA, 1990) 202-223.
16. L. Marini and A. Quarteroni, A relaxation procedure for domain decomposition methods using finite elements, I.A.N. - C.N.R. Publication 577 (1987).
17. A. Mayo, Rapid, high order accurate evaluation of volume integrals of potential theory, J. Comput. Phys. 100 (1992) 236.
18. A. Mayo and A. Greenbaum, Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions, SIAM J. Sci. Statist. Comput. 13 (1992) 101-118.
19. C. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25 (1977) 220-252.
20. H. Schwarz, Über einige Abbidungsaufgaben, Ges. Math. Abh. 11 (1869) 65-83.
21. B.F. Smith, P. Bjørstad and W. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations (Cambridge University Press, Cambridge, 1996).
22. K. Tan, Ph.D. Thesis, Universiteit Utrecht (1995).
23. W. Tang, Generalized Schwarz splittings, SIAM J. Sci. Statist. Comput. 13 (1992) 573-595.
24. H. Zhao, Ph.D. Thesis, UCLA (1996).