Conjugate gradient methods for three-dimensional BEM systems of equations

Engineering Analysis with Boundary Elements

Volumn 30, Issue 6, 2006, Pages 441-449

  Valente, F P ^a   Pina, H L ^b  

^a POLYTECHNIC INSTITUTE OF GUARDA   (Portugal)

^b Instituto Superior Tecnico Institute for Mechanical Engineering   (Portugal)

Author keywords

BEM; Bi conjugate gradient; Bi conjugate gradient stabilized; Conjugate gradient; Conjugate gradient squared; Generalized minimal residual; Iterative techniques.; Preconditioning; Quasi minimal residuals

Indexed keywords

BOUNDARY ELEMENT METHOD; ITERATIVE METHODS; LINEAR ALGEBRA; LINEAR EQUATIONS; PROBLEM SOLVING; THREE DIMENSIONAL;

BI-CONJUGATE GRADIENT; BI-CONJUGATE GRADIENT STABILIZED; CONJUGATE GRADIENT; CONJUGATE GRADIENT SQUARED; GENERALIZED MINIMAL RESIDUAL; PRECONDITIONING; QUASI-MINIMAL RESIDUALS;

GRADIENT METHODS;

EID: 33646813296     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2006.01.015     Document Type: Article

References (26)

1. Brebia C.A., Telles J.C., and Wrobel L.C. Boundary element techniques (1984), Springer, Berlin
2. Leung C.Y., and Walker S.P. Iterative solution of large three-dimensional BEM analyses using GMRES technique. Int J Numer Methods Eng 40 12 (1997) 2227-2236
3. Kane J.H. Boundary element analysis in engineering continuum mechanics (1994), Prentice-Hall, Englewood Cliffs, NJ [chapter 9]
4. Kane J.H., Kumar B.L.K., and Gallagher R.H. Boundary element iterative reanalysis techniques for continuum stuctures. J Eng Mech ASCE 116 10 (1990) 2293-2309
5. Kane J.H., Keyes D.E., and Prasad K.G. Iterative solution techniques in boundary element analysis. Int J Numer Methods Eng 31 (1991) 1511-1536
6. Barra L.P.S., Coutinho A.L.G.A., Mansur W.J., and Telles J.C.F. Iterative solution of BEM equations by GMRES algorithm. Comput Struct 44 (1992) 1249-1253
7. Urekew T.J., and Rencis J. An iterative solution strategy for boundary element equations from mixed boundary value problems. Comput Methods Appl Mech Eng 118 (1994) 13-28
8. Mansur W.J., Araújo F.C., and Malaghini J.E.B. Solution of BEM systems of equations via iterative techniques. Int J Numer Methods Eng 33 (1992) 1823-1841
9. Greenbaum A. Iterative methods for solving linear systems (1997), SIAM, Society for Industrial and Applied Mathematics, Philadelphia, PA
10. Trefethen L.N., and Bau III D. Numerical linear algebra (1997), SIAM, Society for Industrial and Applied Mathematics, Philadelphia, PA
11. Hesteness M.R., and Stiefel E. Methods of conjugate gradients for solving linear systems. J Res Nat Bur Stand 49 (1952) 409-436
12. Saad Y. The Lanczos biorthogonalization algorithm and other oblique projection methods for solving large nonsymmetric systems. SIAM J Numer Anal 19 3 (1982) 485-506
13. Fletcher R. Conjugate gradient methods for indefinite systems. Lecture notes in mathematics vol. 506 (1976), Springer, Berlin p. 73-89
14. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7 3 (1986) 856-869
15. Sonneveld P. CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J Sci Stat Comput 10 1 (1989) 36-52
16. Freund R.W., and Nachtigal N.M. QMR: a quasi-minimal residual method for non-Hermitian linear systems. Numer Math 60 (1991) 315-339
17. Van Der Vorst H.A. Bi-CGStab: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comput 13 2 (1992) 631-644
18. Valente F.P., and Pina H.L.G. Iterative solvers for BEM algebraic systems of equations. Eng Anal Bound Elem 22 2 (1998) 117-125
19. Valente F.P., and Pina H.L.G. Iterative techniques for 3-D boundary element method systems of equations. Eng Anal Bound Elem 25 (2001) 423-429
20. Alléon G., Benzi M., and Giraud L. Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics. Numer Algorithms 16 (1997) 1-15
21. Van Der Vorst H.A. High performance preconditioning, SIAM. J Sci Stat Comput 10 6 (1989) 1174-1185
22. Benzi M. Preconditioning techniques for large linear systems: a survey. J Comput Phys 182 (2002) 418-477
23. Benzi M., and Tuma M. A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM J Sci Comput 19 3 (1998) 968-994
24. Chen K. Matrix preconditioning techniques and applications (2005), Cambridge University Press, Cambridge, MA
25. Meurant G. Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm. Numer Algorithms 22 (1999) 353-365
26. Langtangen H.P. Conjugate Gradient methods and ILU preconditioning of non-symmetric matrix systems with arbitrary sparsity patterns. Int J Numer Methods Fluids 9 (1989) 213-233