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A domain decomposition method based on BEM and FEM for linear exterior boundary value problems. (English) Zbl 0987.65130
The authors design a fairly sophisticated domain decomposition algorithm in order to solve some linear exterior boundary value problems. The algorithm seems to be well suited for parallel processing.

65N38Boundary element methods (BVP of PDE)
65N55Multigrid methods; domain decomposition (BVP of PDE)
65F10Iterative methods for linear systems
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
65Y05Parallel computation (numerical methods)
Full Text: DOI
[1] V. I. Agoshkov, Poincaré--Steklov operators and domain decomposition methods in finite dimensional spaces, inDomain Decomposition Methods for Partial Differential Equations (R. Glowinskiet al., Eds.), pp. 73--112, SIAM, Philadelphia.
[2] Bramble, J. H.; Pasciak, J. E.; Schatz, A. H.: The construction of preconditioners for elliptic problems by substructuring, I. Math. comp. 47, 103-134 (1986) · Zbl 0615.65112
[3] Carstensen, C.; Kuhn, M.; Langer, U.: Fast parallel solvers for symmetric boundary element domain decomposition equations. Numer. math. 79, 321-347 (1998) · Zbl 0907.65119
[4] Costabel, M.: Symmetric methods for the coupling of finite elements and boundary elements. Boundary elements IX, 411-420 (1987)
[5] Gatica, G. N.: Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity. Appl. math. Lett. 10, 29-35 (1997) · Zbl 0895.73066
[6] Gatica, G. N.; Hernández, E. C.; Mellado, M. E.: A domain decomposition method for linear exterior boundary value problems. Appl. math. Lett. 11, 1-9 (1998) · Zbl 0940.65132
[7] Gatica, G. N.; Hsiao, G. C.: On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2. Numer. math. 61, 171-214 (1992) · Zbl 0741.65084
[8] Gatica, G. N.; Hsiao, G. C.: The uncoupling of boundary integral and finite element methods for nonlinear boundary value problems. J. math. Anal. appl. 189, 442-461 (1995) · Zbl 0821.65073
[9] Gatica, G. N.; Hsiao, G. C.: Boundary-field equation methods for a class of nonlinear problems. Pitman research notes in mathematics series 331 (1995) · Zbl 0832.65126
[10] Gatica, G. N.; Mellado, M. E.: Nonoverlapping domain decomposition methods for linear and nonlinear exterior boundary value problems. Proceedings of the fourth world congress on computational mechanics, Buenos Aires, Argentina, June 29--July 2, 1998 (1998) · Zbl 0940.65132
[11] Gatica, G. N.; Wendland, W. L.: Coupling of mixed finite elements and boundary elements for a hyperelastic interface problem. SIAM J. Numer. anal. 34, 2335-2356 (1997) · Zbl 0895.73067
[12] Golub, G. H.; Van Loan, C. F.: Matrix computations. (1983) · Zbl 0559.65011
[13] Han, H.: A new class of variational formulations for the coupling of finite and boundary element methods. J. comput. Math. 8, 223-232 (1990) · Zbl 0712.65093
[14] Han, H.; Wu, X.: The approximation of the exact boundary conditions at an artificial boundary for linear elastic equations and its applications. Math. comp. 59, 21-37 (1992) · Zbl 0754.35008
[15] G. C. Hsiao, B. N. Khoromskij, and, W. J. Wendland, Boundary integral operators and domain decomposition, preprint 94-11, Mathematisches Institut A, Universität Stuttgart, 1994.
[16] G. C. Hsiao, and, W. L. Wendland, Domain Decomposition via Boundary Element Methods, Technical Report, 92-10, Department of Mathematical Sciences, University of Delaware, 1992.
[17] Hsiao, G. C.; Zhang, S.: Optimal order multigrid methods for solving exterior boundary value problems. SIAM J. Numer. anal. 31, 680-694 (1994) · Zbl 0805.65113
[18] Johnson, C.; Nedelec, J. C.: On the coupling of boundary integral and finite element methods. Math. comput. 35, 1063-1079 (1980) · Zbl 0451.65083
[19] Le Tallec, P.: Domain decomposition methods in computational mechanics. Comput. mech. Adv. 1, 121-220 (1994) · Zbl 0802.73079
[20] M. E. Mellado, Numerical Solution of Exterior Problems in Potential Theory and Elasticity, Ph.D. Thesis, Universidad de Concepción, 2000.
[21] Quarteroni, A.; Valli, A.: Theory and application of Steklov--Poincaré operators for boundary value problems. Applied and industrial mathematics, 179-203 (1991)
[22] Quarteroni, A.; Valli, A.: Domain decomposition methods for partial differential equations. (1999) · Zbl 0931.65118
[23] Schmidt, G.: Boundary element discretization of Poincaré--Steklov operators. Numer. math. 69, 83-101 (1994) · Zbl 0827.65118
[24] Smith, B.; Bjorstad, P.; Gropp, W.: Domain decomposition. (1996)
[25] Steinbach, O.: Boundary elements in domain decomposition methods. Contemporary mathematics 180 (1994) · Zbl 0817.65119
[26] Steinbach, O.; Wendland, W. L.: Domain decomposition and preconditioning techniques in boundary element methods. (1997) · Zbl 0884.65113
[27] Wendland, W. L.: On asymptotic error estimates for the combined BEM and FEM. CISM lecture notes 301, 273-333 (1988)
[28] Widlund, O. B.: An extension theorem for finite element spaces with three applications. Numerical techniques in continuum mechaniques (1987) · Zbl 0615.65114