zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Interface relaxation algorithms for BEM-BEM coupling and FEM-BEM coupling. (English) Zbl 1037.65130
Summary: This paper presents several interface relaxation algorithms for boundary element--boundary element coupling (BEM-BEM) and for finite element--boundary element coupling (FEM-BEM). The domain of the original problem is sub-divided into sub-domains, which are modeled by the finite element or boundary element methods. The multi-domain system is coupled using smoothing operators on the inter-domain boundaries. Separate computations for the BEM and FEM sub-domains and successive update of the boundary conditions at the interfaces are performed until convergence is achieved. The interface relaxation coupling algorithms preserve the nature of the FEM and BEM. Further, they do not require any access to the matrices generated by the FEM or BEM and make it easier to utilize different software in different sub-domains.

65N55Multigrid methods; domain decomposition (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N38Boundary element methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
Full Text: DOI
[1] Zienkiewicz, O. C.; Kelly, D. W.; Bettes, P.: The coupling of the finite element method and boundary solution procedures. Int. J. Numer. methods engrg. 11, 355-375 (1977) · Zbl 0347.65048
[2] . Int. J. Boundary element methods commun. 4, No. 2, 58-67 (1993)
[3] . Int. J. Boundary element methods commun. 4, No. 3, 94-104 (1993)
[4] Ganguly, S.; Layton, J. B.; Balakrishma, C.: Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity. Int. J. Numer. methods engrg. 48, 633-654 (2000) · Zbl 0986.74073
[5] Bialecki, R. A.; Ostrowski, Z.; Kassab, A. J.; Yin, Q.; Sciubba, E.: Coupling BEM, FEM and analytic solutions in steady-state potential problems. Engrg. anal. Boundary elem. 26, 597-611 (2002) · Zbl 1011.80006
[6] Elleithy, W. M.; Al-Gahtani, H. J.: An overlapping domain decomposition approach for coupling the finite and boundary element methods. Engrg. anal. Boundary elem. 24, No. 5, 391-398 (2000) · Zbl 1118.76332
[7] Stein, E.; Kreienmeyer, M.: Coupling of BEM and FEM by a multiplicative Schwarz method and its parallel implementation. Engrg. comput. 15, No. 2, 173-198 (1998) · Zbl 0936.74079
[8] Kamiya, N.; Iwase, H.; Kita, E.: Parallel computing for the combination method of BEM and FEM. Engrg. anal. Boundary elem. 18, 221-229 (1996)
[9] Lin, C. -C.; Lawton, E. C.; Caliendo, J. A.; Anderson, L. R.: An iterative finite element--boundary element algorithm. Comput. struct. 39, No. 5, 899-909 (1996) · Zbl 0918.73179
[10] Feng, Y. T.; Owen, D. R. J.: Iterative solution of coupled FE/BE discretization for plate-foundation interaction problems. Int. J. Numer. methods engrg. 39, 1889-1901 (1996) · Zbl 0885.73079
[11] W.M. Elleithy, H.J. Al-Gahtani, M. El-Gebeily, Convergence of the iterative coupling of BEM and FEM, in: 21st World Conference on the Boundary Element Method, BEM21, Oxford University, UK, August 1999, pp. 281--290 · Zbl 1052.76534
[12] Elleithy, W. M.; Al-Gahtani, H. J.; El-Gebeily, M.: Iterative coupling of BE and FE methods in elastostatics. Engrg. anal. Boundary elem. 25, No. 8, 685-695 (2001) · Zbl 1003.74501
[13] El-Gebeily, M.; Elleithy, W. M.; Al-Gahtani, H. J.: Convergence of the domain decomposition finite element--boundary element coupling methods. Comput. methods appl. Mech. engrg. 191, No. 43, 4851-4867 (2002) · Zbl 1027.65139
[14] Kamiya, N.; Iwase, H.; Kita, E.: Parallel implementation of boundary element method with domain decomposition. Engrg. anal. Boundary elem. 18, 209-216 (1997)
[15] Mu, M.: Solving composite problems with interface relaxation. SIAM J. Sci. comput. 20, No. 4, 1394-1416 (1999) · Zbl 0941.65125
[16] Funaro, D.; Quarteroni, A.; Zanolli, P.: An interface procedure with interface relaxation for domain decomposition methods. SIAM J. Numer. anal. 25, No. 6, 1213-1236 (1988) · Zbl 0678.65082
[17] Lions, P. L.: On the Schwarz alternating method: a variant for nonoverlapping subdomains. Domain decomposition methods for partial differential equations, 202-223 (1990)
[18] Mu, M.; Rice, J. R.: Modeling with collaborating PDE solvers----theory and practice. Comput. syst. Engrg. 6, 87-95 (1995)
[19] Rice, J. R.; Tsompanopoulou, P.; Vavalis, E. A.: Interface relaxation methods for elliptic differential equations. Appl. numer. Math. 32, 219-245 (1999) · Zbl 0942.65138