Optimization based domain decomposition method for partial differential equations

Computers and Mathematics with Applications

Volumn 37, Issue 10, 1999, Pages 77-93

  Gunzburger, M D ^a   Peterson, J S ^a   Kwon, H ^b  

^a IOWA STATE UNIVERSITY   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; OPTIMIZATION; PROBLEM SOLVING;

DOMAIN DECOMPOSITION METHODS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0033130831     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(99)00127-3     Document Type: Article

References (18)

1. T. Chan, D. Keyes, G. Meurant, J. Scroggs and R. Voigt, Proc. Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, (1992).
2. T. Chan, R. Glowinski, J. Periaux, and O. Widlund, Proc. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, (1990).
3. T. Chan, G. Meurant, J. Periaux and O. Widlund, Domain Decomposition Methods, SIAM, Philadelphia, (1989).
4. R. Glowinski, G. Golub, G. Meurant and J. Periaux, Proc. First International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, (1988).
5. R. Glowinski, Y. Kuznetsov, G. Meurant, J. Periaux and O. Widlund, Proc. Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, (1991).
6. D. Keyes and J. Xu, Domain Decomposition Methods in Scientific and Engineering Computing, AMS, Providence, RI, (1994).
7. C. Farhat and F.-X. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithms, Int. J. Numer. Meth. Engrg. 32, 1205-1227, (1991).
8. C. Farhat and F.-X. Roux, An unconventional domain decomposition method for an efficient parallel solution of large-scale finite element problems, SIAM J. Sci. Stat. Comput. 13, 379-396, (1992).
9. R. Glowinski and P. Le Tallec, Augmented lagrangian interpretation of the nonoverlapping Schwarz alternating method, in Proc. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, (Edited by T. Chan, R. Golwinski, J. Periaux and O. Widlund), pp. 224-231, SIAM, Philadelphia, PA, (1990).
10. R. Glowinski and M. Wheeler, Domain decomposition and mixed finite element methods for elliptic problems, in Proc. First International Symposium on Domain Decomposition Methods for Partial Differential Equations, (Edited by R. Glowinski, G. Golub, G. Meurant and J. Periaux), pp. 144-172, SIAM, Philadelphia, PA, (1988).
11. J. Mandel and R. Rezaur, Convergence of a Substructuring Method with Lagrange Multipliers (to appear).
12. P. Ciarlet, Finite Element Methods for Elliptic Problems, North-Holland, Amsterdam, (1978).
13. V. Tikhomirov, Fundamental Principles of the Theory of Extremal Problems, Wiley, New York, (1986).
14. P. Cuvelier, Optimal control of a system governed by the navier-stokes equations coupled with the heat equations, in New Developments in Differential Equations, pp. 81-98, North-Holland, (1976).
15. M. Gunzburger, L. Hou and T. Svobdny, Heating and cooling control of temperature distributions along boundaries of flow domains, J. Math. Sys. Estim. Cont. 3, 147-172, (1993).
16. F. Brezzi, J. Rappaz and P.-A. Raviart, Finite-dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions, Numer. Math. 36, 1-25, (1980).
17. V. Girault and P.-A. Raviart, Finite Element Approximation of the Navier-stokes Equations, Springer, Berlin, (1979).
18. P. Ciarlet, Introduction to Linear Algebra and Optimization, Cambridge, Cambridge, (1989).