3D Helmholtz wave equation by fictitious domain method

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 13, Issue 5, 1998, Pages 371-387

  Kuznetsov, Yu A ^a   Lipnikov, K N ^a  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001354931     PISSN: 09276467     EISSN: None     Source Type: Journal    
DOI: 10.1515/rnam.1998.13.5.371     Document Type: Article

References (24)

1. G. P. Astrakhantsev, Iterative methods for solving variational difference schemes for two dimensional second-order elliptic equations. PhD thesis, LOMI of the USSR Acad. Sci., Leningrad, 1972 (in Russian).
2. C. Atamian, Q. V. Dinh, R. Glowinski, He Jiwen, and J. Periaux, Control approach to fictitious-domain methods application to fluid dynamics and electro-magnetics. In: Proc. Symp. 'Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations'. Moscow, 1990, pp. 275-309 (1991).
3. A. Bayliss and E. Turkel, Radiation boundary conditions for wave-like equations. Commun. Pure Appl. Math. (1980) 33, 707-725.
4. A. N. Bespalov, Application of fictitious domain method to solving the Helmholtz wave equation in unbounded domain. INRIA report No. 1797, 1992.
5. A. N. Bespalov, Solution of 3D electromagnetic problems by algebraic fictitious domain method. Proc. of the 2nd ECCOMAS Conference on Numerical Methods in Engineering, Paris, France, September 9-13, 1996. Wiley & Sons, 1996, pp. 567-572.
6. P. G. Ciarlet and J.-L. Lions, Handbook of Numerical Analysis. Vol. II: Finite element methods (Part 1). North-Holland, Amsderdam, 1991.
7. B. Engquist and A. Majda, Radiation boundary conditions for acoustic and elastic calculations. Commun. Pure Appl. Math. (1979) 32, 313-357.
8. O. G. Ernst, A finite-element capacitance matrix method for exterior Helmholtz problems. Numer. Math. (1996) 75, 175-204.
9. S. A. Flnogenov and Yu. A. Kuznetsov, Two-stage fictitious components method for solving the Dirichlet boundary value problem. Sov. J. Numer. Anal. Math. Modelling (1988) 3, 301-323.
10. D. Givoli, Non-reflecting boundary conditions. J. Comput. Phys. (1991) 94, 1-29.
11. C. I. Goldstein, The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem. Numer. Math. (1981) 38, 61-82.
12. C. I. Goldstein, The solution of exterior interface problems using a variational method with Lagrange multipliers. J. Math. Anal, and Appl. (1983) 97, 480-508.
13. Yu. A. Kuznetsov, Matrix computational processes in subspaces. In: Computing methods in applied sciences and engineering VI, Proc. 6th Int. Symp. Versailles, 1983, pp. 15-31 (1984).
14. Yu. A. Kuznetsov, Numerical methods in subspaces. In: Computational Processes and Systems (1984), 2, 265-350 (in Russian).
15. Yu. A. Kuznetsov and K. N. Upnikov, Fictitious domain methods for solving the Helmholtz wave equation in unbounded domains, In: 'Numerical Methods and Mathematical Modelling'. Moscow, OVM Rus. Acad. Sci., 1993, pp. 56-71 (in Russian).
16. Yu. A. Kuznetsov and A. M. Matsokin, On partial solution of systems of linear algebraic equations. Sov. J. Numer. Anal. Math. Modelling (1989) 4, No. 6, 453-467.
17. Yu. A. Kuznetsov and O. D. Trufanov, Two-stage fictitious components method for solving the wave Helmholtz equation. Sov. J. Numer. Anal. Math. Modelling (1988) 3, No. 5, 373-392.
18. G. I. Marchuk and Yu. A. Kuznetsov, Some aspects of iterative methods, In: Computational Methods of Linear Algebra (Ed. G. I. Marchuk). Novosibirsk Comp. Centre of the USSR Acad. Sci., Novosibirsk, 1972, pp. 4-20 (in Russian).
19. G. I. Marchuk, Yu. A. Kuznetsov, and A. M. Matsokin, Fictitious domain and domain decomposition methods. Sov. J. Numer. Anal. Math. Modelling (1986) 1, 3-35.
20. W. Proskurowski and O. Widlund, On the numerical solution of Helmholtz's equation by the capacitance matrix method. Math. Comput. (1976) 30, 433-468.
21. Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. (1986) 7, 856-869.
22. A. Schatz, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms. Math. Comp. (1974) 28, 959-962.
23. A. V. Supalov, Development of algorithms for generating 3D locally Gtted grids and their program realization. PhD thesis, Moscow, Institute of Numerical Mathematics RAN, 1994 (in Russian).
24. P. N. Swarztrauber, The method of cyclic reduction, Fourier analysis and the FACR algorithm for the solution of elliptic partial differential equations. SIAM Review (1977) 19, 490-501.