A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. Part 2: Neumann boundary conditions

International Journal for Numerical Methods in Engineering

Volumn 58, Issue 1, 2003, Pages 63-81

  Hetmaniuk, U ^a   Farhat, C ^a  

^a University of Colorado   (United States)

Author keywords

Acoustic scattering; Domain decomposition; Fictitious method; Fourier finite elements; Neumann boundary condition

Indexed keywords

BOUNDARY CONDITIONS; PARTIAL DIFFERENTIAL EQUATIONS; SCATTERING;

DOMAIN DECOMPOSITION;

ACOUSTICS;

ACOUSTIC WAVE; FINITE ELEMENT METHOD; SUBMARINE; WAVE SCATTERING;

EID: 0141795689     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.758     Document Type: Article

References (22)

1. Wilson E. Structural analysis of axisymmetric solids. AIAA Journal 1965; 3:2269-2274.
2. Mercier B, Raugel G. Résolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et séries de Fourier en χ. R.A.I.R.O. Analyse Numérique 1982; 16(4):405-461.
3. Bernardi C, Dauge M, Maday Y. Spectral Methods for Axisymmetric Domains. Gauthier-Villars: Paris, 1999.
4. Farhat C, Hetmaniuk U. A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. Pan 1: Dirichlet boundary conditions. International Journal for Numerical Methods in Engineering 2002; 54-1309-1332.
5. Hetmaniuk U, Farhat C. A blended fictitious/real domain decomposition method for partially axisymmetric exterior Helmholtz problems with Dirichlet boundary conditions. In Recent Developments in Domain Decomposition Methods, Pavarino L, Toselli A (eds). Springer: Berlin, 2002; 1-26.
6. Proskurowski W, Widlund O. On the numerical solution of Helmholtz's equation by the capacitance matrix method. Mathematics of Computation 1976; 30:433-468.
7. Astrakhantsev GP. Methods of fictitious domains for a second-order elliptic equation with natural boundary conditions. U.S.S.R. Computational Mathematics and Mathematatical Physics, 1978; 18:114-121.
8. Marchuk GI, Kuznetsov YA, Matsokin AM. Fictitious domain and domain decomposition methods. Soviet Journal of Numerical Analysis and Mathematical Modelling 1986; 1:3-36.
9. Atamian C, Dihn QV, Glowinski R, He J, Périaux J. On some embedding methods applied to fluid dynamics and electromagnetics. Computer Methods in Applied Mechanics and Engineering 1991; 91:1271-1299.
10. Glowinski R, Pan TW, Périaux J. A fictitious domain method for Dirichlet problem and applications. Computer Methods in Applied Mechanics and Engineering 1994; 111:283-303.
11. Heikkola E, Kuznetsov YA, Neittaanmäki P, Toivanen J. Fictitious domain methods for the numerical solution of two-dimensional scattering problems. Journal of Computational Physics 1998; 145:89-109.
12. Joly P, Rhaouti L. Domaines fictifs, éléments finis H(div) et condition de Neumann: le problème de la condition inf-sup. Comptes Rendus des Séances de l'Académie des Sciences, Série I 1999; 328(12):1225-1230.
13. Quarteroni A, Valli A. Domain Decomposition Methods for Partial Differential Equations. Oxford University Press: New-York, 1999.
14. Dean EJ, Dihn QV, Glowinski R, He J, Pan TW. Périaux J. Least squares/domain embedding methods for Neumann problems: applications to fluid dynamics. In Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Keyes DE, Chan TF, Meurant GA, Scroggs JS, Voigt RG (eds). SIAM: Philadelphia, 1992; 451-475.
15. Antoine X, Barucq H, Bendali A. Bayliss-Turkel like radiation conditions on surfaces of arbitrary shape. Journal of Mathematical Analysis and Applications 1999; 229(1):184-211.
16. Tezaur R, Macedo A, Farhat C, Djellouli R. Three-dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries. International Journal for Numerical Methods in Engineering 2002; 53:1461-1476.
17. Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods, Springer: Berlin, 1991.
18. Girault V, Glowinski R. Error analysis of a fictitious domain method applied to a Dirichlet problem. Japan Journal of Industrial and Applied Mathematics 1995; 12:487-514.
19. Farhat C, Macedo A, Lesoinne M. A two-level domain decomposition method for the iterative solution of high-frequency exterior Helmholtz problems. Numerische Mathematik 2000; 85:283-303.
20. Farhat C. Redesigning the skyline solver for parallel/vector supercomputers. International Journal of High Speed Computing 1990; 2(3):223-238.
21. Börgers C, Widlund O. On finite element domain embedding methods. SIAM Journal on Numerical Analysis 1990; 27:963-978.
22. Dautray R, Lions JL. Mathematical Analysis and Numerical Methods for Science and Technology. Springer: Berlin, 1988-1993.