A domain decomposition method for the exterior Helmholtz problem

Journal of Computational Physics

Volumn 147, Issue 2, 1998, Pages 388-401

  Susan Resiga, Romeo F ^a   Atassi, Hafiz M ^a  

^a University of Notre Dame   (United States)

Author keywords

Domain decomposition; Exterior problem; Finite element method; Helmholtz equation; Nonreflecting boundary conditions

Indexed keywords

FINITE ELEMENT METHOD; ITERATIVE METHODS;

CONDITION; DIRICHLET-TO-NEUMANN MAP; DOMAIN DECOMPOSITIONS; DOMAIN-DECOMPOSITION METHODS; EXTERIOR PROBLEM; HELMHOLTZ PROBLEMS; HELMHOLTZ'S EQUATIONS; NON REFLECTING BOUNDARY CONDITION; NONLOCAL; SUBDOMAIN BOUNDARY;

DOMAIN DECOMPOSITION METHODS;

EID: 0040683523     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6094     Document Type: Article

References (16)

1. Després B. Décomposition de domaine et problème de Helmholtz. C.R. Acad. Sci. Paris. 311:1990;313.
2. Atassi H. M. Unsteady aerodynamics of vortical flows: Early and recent developments. Aerodynamics and Aeroacoustics. 1994;121.
3. Lyrintzis A. S. Review: The use of Kirchhoff's method in computational aeroacoustics. J. Fluids Eng. 116:1994;665.
4. Atassi H. M., Dusey M. P., Davis C. M. Acoustic radiation from a thin airfoil in nonuniform subsonic flows. AIAA J. 31:1993;12.
5. Scott J. R., Atassi H. M. A finite-difference, frequency-domain numerical scheme for the solution of the gust response problem. J. Comput. Phys. 119:1995;75.
6. C. M. Davis, H. M. Atassi, The far field acoustic pressure of an airfoil in nonuniform subsonic flows, ASME Symposium on Flow Noise Modeling, Measurement, and Control, NCA, 1991, 11, 107.
7. S. M. Patrick, C. M. Davis, H. M. Atassi, Acoustic radiation from a lifting airfoil in nonuniform subsonic flows, Computational Aero- and Hydro-acoustics, ASME-FED, 1993, 147, R. R. MankbadiA. S. LyrintzisO. BaysalL. A. PovinelliM. Y. Hussaini, 41.
8. Lamb H. Hydrodynamics. 1906.
9. Keller J. B., Givoli D. Exact Non-reflecting boundary conditions. J. Comput. Phys. 82:1989;172.
10. Harari I., Hughes T. J. R. Analysis of continuous formulations underlying the computation of time-harmonic acoustics in exterior domains. Comput. Methods Appl. Mech. Eng. 97:1992;103.
11. Grote M. J., Keller J. B. On nonreflecting boundary conditions. J. Comput. Phys. 122:1995;231.
12. Ernst O. G. A finite-element capacitance matrix method for exterior Helmholtz problems. Numer. Math. 75:1996;175.
13. Givoli D. Numerical Methods for Problems in Infinite Domains. 33:1992.
14. Malhotra M., Pinsky P. M. A matrix-free interpretation of the nonlocal Dirichlet-to-Neumann radiation boundary condition. Int. J. Num. Meth. Eng. 39:1996;3705.
15. Benamou J. D., Després B. A domain decomposition method for the Helmholtz equation and related optimal control problems. J. Comput. Phys. 136:1997;68.
16. X.-C. Cai, M. Casarin, F. Elliott, O. B. Widlund, Overlapping Schwarz algorithms for solving Helmholtz's equation, Proc. 10th Int. Conf. on Domain Decomposition Methods, Providence, 1998, X.-C. CaiC. FahratJ. Mandel.