Finite element schemes for non-linear problems in infinite domains

International Journal for Numerical Methods in Engineering

Volumn 42, Issue 2, 1998, Pages 341-360

  Givoli, Dan ^a   Patlashenko, Igor ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Dirichlet to neumann (dtn); Finite element; Infinite domain; Non linear elliptic problems

Indexed keywords

COMPUTATIONAL METHODS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

DIRICHLET TO NEUMANN (DTN) FINITE ELEMENT METHOD; NONLINEAR ELLIPTIC PROBLEMS;

FINITE ELEMENT METHOD;

EID: 0032073499     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980530)42:2<341::AID-NME371>3.0.CO;2-5     Document Type: Article

References (58)

1. D. Givoli, Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992.
2. D. Givoli, 'Non reflecting boundary conditions', J. Comput. Phys., 94, 1-29 (1991).
3. B. Gustafsson and H.-O. Kreiss, 'Boundary conditions for time dependent problems with an artificial boundary', J. Comput. Phys., 30, 333-351 (1979).
4. L. Ferm and B. Gustafsson, 'A down-stream boundary procedure for the Euler equations', Comput. Fluids, 10, 261-276 (1982).
5. T. Hagstrom and H. B. Keller, 'Exact boundary conditions at an artificial boundary for partial differential equations in cylinders', SIAM J. Math. Anal., 17, 322-341 (1986).
6. T. Hagstrom and H. B. Keller, 'Asymptotic boundary conditions and numerical methods for non-linear elliptic problems on unbounded domains', Math. Comput., 48, 449-470 (1987).
7. T. Hagstrom, 'Boundary conditions at outflow for a problem with transport and diffusion', J. Comput. Phys., 69, 69-80 (1987).
8. S. Buonincontri and T. Hagstrom, 'Multidimensional traveling wave solutions to reaction-diffusion equations', IMA J. Appl. Math., 43, 261-271 (1989).
9. T. Hagstrom, 'Asymptotic boundary conditions for dissipative waves: general theory', Math. Comput., 56, 589-606 (1991).
10. T. Hagstrom, 'Conditions at the downstream boundary for simulations of viscous, incompressible flow', SIAM J. Sci. Statist. Comput., 12, 843-858 (1991).
11. L. Ting and M. J. Miksis, 'Exact boundary conditions for scattering problems', J. Acoust. Soc. Am., 80, 1825-1827 (1986).
12. D. Givoli and D. Cohen, 'Non-reflecting boundary conditions based on Kirchhoff-type formulae', J. Comput. Phys., 117, 102-113 (1995).
13. M. J. Grote and J. B. Keller, 'Exact nonreflecting boundary conditions for the time dependent wave equation', SIAM J. Appl. Math., 55, 280-297 (1995).
14. M. J. Grote and J. B. Keller, 'Nonreflecting boundary conditions for time dependent scattering', J. Comput. Phys., 127, 52-65 (1996).
15. S. V. Tsynkov, 'An application of nonlocal external conditions to viscous flow computations', J. Comput. Phys., 116, 212-225 (1995).
16. V. S. Ryaben'kii and S. V. Tsynkov, 'Artificial boundary conditions for the numerical solution of external viscous flow problems', SIAM J. Numer. Anal., 32, 1355-1389 (1995).
17. S. V. Tsynkov, E. Turkel and S. Abarbanel, 'External flow computations using global boundary conditions', AIAA J., 34, 700-706 (1996).
18. J. B. Keller and D. Givoli, 'Exact non-reflecting boundary conditions', J. Comput. Phys., 82, 172-192 (1989).
19. D. Givoli and J. B. Keller, 'A finite element method for large domains', Comput. Meth. Appl. Mech. Engng., 76, 41-66 (1989).
20. D. Givoli and J. B. Keller, 'Non-reflecting boundary conditions for elastic waves', Wave Motion, 12, 261-279 (1990).
21. D. Givoli, 'A combined analytic-finite element method for elastic shells', Int. J. Solids Struct., 26, 185-198 (1990).
22. D. Givoli and S. Vigdergauz, 'Artificial boundary conditions for 2D problems in geophysics', Comput. Meth. Appl. Mech. Engng., 110, 87-101 (1993).
23. I. Patlashenko and D. Givoli, 'Nonlocal and local artificial boundary conditions for two-dimensional flow in an infinite channel', Int. J. Numer. Meth. Heat and Fluid Flow, 6, 47-62 (1996).
24. D. Givoli, 'A spatially exact non-reflecting boundary condition for time dependent problems', Comput. Meth. Appl. Mech. Engng., 95, 97-113 (1992).
25. I. Harari and T. J. R. Hughes, 'Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains', Comput. Meth. Appl. Mech. Engng., 98, 411-454 (1992a).
26. I. Harari and T. J. R. Hughes, 'Analysis of continuous formulations underlying the computation of time-harmonic acoustics in exterior domains', Comput. Meth. Appl. Mech. Engng., 97, 103-124 (1992b).
27. M. J. Grote and J. B. Keller, 'On nonreflecting boundary conditions', J. Comput. Phys., 122, 231-243 (1995).
28. M. Malhotra and P. M. Pinsky, 'A matrix-free interpretation of the non-local Dirichlet-to-Neumann radiation boundary condition', Int. J. Numer. Meth. Engng., 39, 3705-3713 (1996).
29. R. J. Astley, 'FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach', Commun. Numer. Meth. Engng., 12, 257-267 (1996).
30. R. C. MacCamy and S. P. Marin, 'A finite element method for exterior interface problems', Int. J. Meth. Math. Sci., 3, 311-350 (1980).
31. C. I. Goldstein, 'A finite element method for solving Helmholtz type equations in wave guides and other unbounded domains', Math. Comput., 39, 309-324 (1982).
32. A. Bayliss, C. I. Goldstein and E. Turkel, 'The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics', Comp. Math. Appl., 11, 655-665 (1985).
33. C. Canuto, S. I. Hariharan and L. Lustman, 'Spectral methods for exterior elliptic problems', Numer. Math., 46, 505-520 (1985).
34. M. Masmoudi, 'Numerical solution of exterior problems', Numer. Math., 51, 87-101 (1987).
35. M. Lenoir and A. Tounsi, 'The localized finite element method and its application to the 2D sea-keeping problem', SIAM J. Numer. Anal., 25, 729-752 (1988).
36. S. W. Marcus, 'A generalized impedance method for application of the parabolic approximation to underwater acoustics', J. Acoust. Soc. Am., 90, 391-398 (1991).
37. M. Verriere and M. Lenoir, 'Computation of waves generated by submarine landslides', Int. J. Numer. Meth. Fluids, 14, 403-121 (1992).
38. G. N. Gatica and G. C. Hsiao, 'The coupling of boundary integral and finite element methods for nonmonotone non-linear problems', Numer. Func. Anal. Optim., 13, 431-447 (1992).
39. 2', Numer. Math., 61, 171-214 (1992).
40. B. Engquist and A. Majda, 'Numerical radiation boundary conditions for unsteady transonic flow', J. Comp. Phys., 40, 91-103 (1981).
41. Thomas and M. D. Salas, 'Far field boundary conditions for transonic lifting solutions to the Euler equations', AIAA J., 24, 1074-1080 (1986).
42. T. Hagstrom and S. I. Hariharan, 'Accurate boundary conditions for exterior problems in gas dynamics', Math. Comput., 51, 581-97 (1988).
43. W.-S. Don and D. Gottlieb, 'Spectral simulations of an unsteady compressible flow past a circular cylinder', Comput. Meth. Appl. Mech. Engng., 80, 39-58 (1990).
44. S. Abarbanel, W.-S. Don, D. Gottlieb, D. H. Rudy and J. C. Townsend, 'Secondary frequencies in the wake of a circular cylinder with vortex shedding', J. Fluid Mech., 225, 557-574 (1991).
45. A. Verhoff and D. Stookesberry, 'Second-order far-field computational boundary conditions for inviscid duct flow problems', AIAA J., 30, 1268-1276 (1992).
46. R. A. Pearson, 'Consistent boundary conditions for the numerical models of systems that admit dispersive waves', J. Atmos. Sci., 31, 1418-1489 (1974).
47. L. Halpern and M. Schatzman, 'Artificial boundary conditions for viscous incompressible flows', SIAM J. Math. Anal., 20, 308-353 (1989).
48. G. Jin and M. Braza, 'A nonreflecting outlet boundary condition for incompressible unsteady Navier-Stokes calculations', J. Comput. Phys., 107, 239-253 (1993).
49. J. S. Danowitz, S. A. Abarbanel and E. Turkel, 'A far-field non-reflecting boundary condition for two-dimensional wake flows', ICASE Rep. 95-63, NASA Langley, Hampton, VA, 1995.
50. G. W. Hedstrom, 'Nonreflecting boundary conditions for non-linear hyperbolic systems', J. Comp. Phys., 30, 222-237 (1979).
51. K. W. Thompson, 'Time dependent boundary conditions for hyperbolic systems', J. Comp. Phys., 68, 1-24 (1987).
52. B. Gustafsson, 'Far-field boundary conditions for time-dependent hyperbolic systems', SIAM J. Sci. Stat. Comput., 9, 812-828 (1988).
53. K. W. Thompson, 'Time dependent boundary conditions for hyperbolic systems, II', J. Comp. Phys., 89, 439-461 (1990).
54. S. Kami, 'Far-field filtering operators for suppression of reflections from artificial boundaries', SIAM J. Numer. Anal., 33, 1014-1047 (1996).
55. M. Van Dyke, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, CA, 1975.
56. D. Givoli, I. Patlashenko and J. B. Keller, 'High order boundary conditions and finite elements for infinite domains', Comp. Meth. Appl. Mech. Engng., 143, 13-39 (1997).
57. P. J. Davis and P. Rabinowitz, Methods of numerical integration, 2nd edn, Academic Press, New York, 1984.
58. I. Patlashenko and D. Givoli, 'A numerical method for problems in infinite strips with irregularities extending to infinity', Numerical Methods for POEs, in press.