Bi-CG: An effective solver for three fields domain decomposition method in parallel environments After applying the substructuring preconditioner for a linear system stemming from the three fields domain decomposition method for elliptic boundary value problems, the preconditioned system will be nonsymmetric and the bi-conjugate gradient (Bi-CG) method can be applied. We show that in parallel environments the Bi-CG method works as preconditioned conjugate gradient (PCG) method which was applied by S. Bertoluzza [Math. Comp. 73, No. 246, 659–689 (2003)], and in this case extensive numerical tests, performed on both conforming and nonconforming formulation, show that Bi-CG can work faster than PCG

References in zbMATH (referenced in 34 articles , 1 standard article )

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  1. Sogabe, T.; Sugihara, M.; Zhang, S.-L.: An extension of the conjugate residual method to nonsymmetric linear systems (2009)
  2. Ginkin, V. P.; Ganina, S. M.; Chernov, K. G.: Optimal preconditioner for the biconjugate gradient method (2008)
  3. Sonneveld, Peter; van Gijzen, Martin B.: IDR((s)): A family of simple and fast algorithms for solving large nonsymmetric systems of linear equations (2008)
  4. Mokhtarzadeh, M. R.; Mokhtary, R.; Chegini, N. G.: Bi-CG: An effective solver for three fields domain decomposition method in parallel environments (2006)
  5. Valente, F. P.; Pina, H. L.: Conjugate gradient methods for three-dimensional BEM systems of equations (2006)
  6. Ding, D. Z.; Chen, R. S.; Wang, D. X.; Yung, Edward K. N.; Chan, C. H.: The application of the generalized product-type method based on Bi-CG to accelerate the sparse-matrix/canonical grid method (2005)
  7. Schenk, O.; van der Vorst, H. A.: Solution of linear system (2005)
  8. Fasano, Giovanni: Conjugate gradient (CG)-type method for the solution of Newton’s equation within optimization frameworks (2004)
  9. Wang, C.; Khoo, B. C.: An indirect boundary element method for three-dimensional explosion bubbles. (2004)
  10. van der Vorst, Henk A.: Iterative Krylov methods for large linear systems (2003)
  11. Yang, Zhongchao: The parallel computation of steady Navier-Stokes equations with Bi-CG iterative method based on EBE technique. (2002)
  12. Guo, Xinglin; Sha, Desong; Zhang, Zhongding; Wu, Chengwei: Viscoplasticity model for numerical simulation of Bingham fluid flow (2000)
  13. Sidi, Avram; Kluzner, Vladimir: A Bi-CG type iterative method for Drazin-inverse solution of singular inconsistent nonsymmetric linear systems of arbitrary index (2000)
  14. Papadakis, G.; Bergeles, G.: A local grid refinement method for three-dimensional turbulent recirculating flows (1999)
  15. Zhao, Jiabao; Sheng, Zhaohan: An improved conjugate gradient square algorithm (1999)
  16. Valente, F. P.; Pina, H. L. G.: Iterative solvers for BEM algebraic systems of equations (1998)
  17. Van der Vorst, H. A.; Sleijpen, G. L. G.: Iterative Bi-CG type methods and implementation aspects (1998)
  18. Cao, Zhihao: Avoiding breakdown in variants of the BI-CGSTAB algorithm (1997)
  19. Zhang, Shao-Liang: GPBi-CG: Generalized product-type methods based on Bi-CG for solving nonsymmetric linear systems (1997)
  20. Fokkema, Diederik R.; Sleijpen, Gerard L. G.; Van der Vorst, Henk A.: Generalized conjugate gradient squared (1996)

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