Journal of Scientific Computing

, Volume 10, Issue 3, pp 289–304 | Cite as

Spectral multidomain approximation of elliptic problems with mixed conditions on the interfaces

  • F. Pasquarelli
Article
  • 46 Downloads

Abstract

The multidomain technique for elliptic problems, that allows the fulfillment of the interface conditions by means of a suitable combination of the continuity of the solution and of its normal derivative, is considered. Some choices of this combination are investigated and, in particular, a choice that allows the solution of the multidomain problem through two solutions for each subproblem, is proposed. The scheme has been discretized with a collocation method and some numerical tests are reported. Moreover the method is compared with the more classical Dirichlet/Neumann one as well as with the capacitance matrix method.

Key words

Spectral method elliptic multidomain method parallel computation 

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References

  1. Bernardi, C., Debit, N., and Maday, Y. (1990). Coupling finite element and spectral methods: first results.Math. Comp. 54, 21–39.Google Scholar
  2. Bernardi, C., Maday, Y., and Sacchi-Landriani, G. (1990). Nonconforming matching conditions for coupling spectral and finite element methods.Appl. Num. Math. 6, 65–84.Google Scholar
  3. Brambilla, A., Carlenzoli, C., Gazzaniga, G., Gervasio, P., and Sacchi, G. (1992). Implementation of Domain Decomposition Techniques on nCUBE2 parallel machine. In Quarteroni, A.et al. (ed.),Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia.Google Scholar
  4. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988).Spectral Methods in Fluid Dynamics. Springer Verlag.Google Scholar
  5. Carlenzoli, C., and Gervasio, P. (1992). Effective numerical algorithms for the solution of algebraic systems arising in spectral methods.Applied Numerical Mathematics 10, 87–113.Google Scholar
  6. Davis, P. J., and Rabinowitz, P. (1984).Methods of Numerical Integration. Academic Press, London, New York.Google Scholar
  7. Frati, A., Pasquarelli, F., and Quarteroni, A. (1993). Spectral approximation to advection-diffusion problems by the fictitious interface method.J. Comput. Phys. 107(2), 201–211.Google Scholar
  8. Funaro, D., Quarteroni, A., and Zanolli, P. (1988). An iterative procedure with interface relaxation for domain decomposition methods.SIAM J. Numer. Anal. 25, 1213–1236.Google Scholar
  9. Givois, E. (1992). Etude et implémentation de deux méthodes de décomposition de domaines. PhD thesis, Université Paris Dauphine.Google Scholar
  10. Lions, P. L. (1990). On the Schwarz alternating method III: a variant for nonoverlapping subdomains. In Periaux, J., Chan, T. F., Glowinski, R., and Widlund, O. B. (eds.),Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, pp. 202–231.Google Scholar
  11. Marini, L. D., and Quarteroni, A. (1989). A relaxation procedure for domain decomposition methods using finite elements.Numer. Math. 55, 575–598.Google Scholar
  12. Quarteroni, A. (1991). Domain Decomposition and Parallel Processing for the Numerical Solution of Partial Differential Equations.Surv. Math. Industry 1, 75–118.Google Scholar
  13. Quarteroni, A. (ed.) (1994). Domain Decomposition Methods in Science and Engineering. AMS, Providence, Rhodes Island.Google Scholar
  14. Quarteroni, A., and Sacchi Landriani, G. (1988). Parallel Algorithms for the Capacitance Matrix Method in Domain Decompositions.Calcolo 25(1, 2), 75–102.Google Scholar
  15. Quarteroni, A., Pasquarelli, F., and Valli, A. (1992). Heterogeneous domain decomposition: principles, algorithms, applications. In Keyes, D. E., Chan, T. F., Meurant, G., Scroggs, J. S., and Voigtd, R. G. (eds.),Fifth Int'l. Symp. on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, pp. 129–150.Google Scholar
  16. Quarteroni, A., and Valli, A. (1994).Numerical Approximation of Partial Differential Equations. Springer Verlag, Heidelberg.Google Scholar
  17. Sacchi Landriani, G., Gastaldi, F., and Quarteroni, A. (1990). On the coupling of two dimensional hyperbolic and elliptic equations: analytical and numerical approach. In Periaux, J., Chan, T. F., Glowinski, R., and Widlund, O. B. (eds.),Third Int'l. Symp. on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, pp. 22–63.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • F. Pasquarelli
    • 1
  1. 1.Dipartimento di MatematicaUniversità Cattolica Via Trieste 17BresciaItaly

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