Preconditioners in computational geomechanics: A survey

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 35, Issue 9, 2011, Pages 980-996

  Gambolati, G ^a   Ferronato, M ^a   Janna, C ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Contact mechanics; Coupled consolidation; Iterative solver; Preconditioning

Indexed keywords

COMPUTATIONAL GEOMECHANICS; CONTACT MECHANICS; COUPLED CONSOLIDATION; DIAGONAL SCALING; FINITE ELEMENTS; FULLY-COUPLED; GRADIENT-LIKE; INCOMPLETE FACTORIZATION; INCOMPLETE LU-DECOMPOSITION; ITERATIVE SOLVERS; KRYLOV SUBSPACE; LINEAR SOLVER; MIXED CONSTRAINTS; NUMERICAL RESULTS; PRECONDITIONERS; PRECONDITIONING;

CONJUGATE GRADIENT METHOD; FINITE ELEMENT METHOD;

SURVEYS;

ALGORITHM; COMPARATIVE STUDY; CONSOLIDATION; DECOMPOSITION ANALYSIS; EFFICIENCY MEASUREMENT; FINITE ELEMENT METHOD; GEOMECHANICS; NUMERICAL MODEL; PERFORMANCE ASSESSMENT;

EID: 79958812199     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.937     Document Type: Article

References (42)

1. Saad Y, Van der Vorst HA. Iterative solution to linear systems in the 20th century. Journal of Computational and Applied Mathematics 2000; 23:1-33.
2. Van der Vorst HA. Iterative Krylov Methods for Large Linear Systems. Cambridge University Press: Cambridge, 2003.
3. Freund RW, Nachtigal NM. A new Krylov subspace method for symmetric indefinite linear systems. Proceedings of 14th IMACS World Conference on Computational and Applied Mathematics, Atlanta, Georgia, 1994; 1253-1256.
4. Freund RW, Nachtigal NM. QMR: a quasi-minimal residual method for non-Hermitian linear systems. Numerische Mathematik 1991; 60:315-339.
5. Hladik I, Reed MB, Swoboda G. Robust preconditioners for linear elasticity FEM analyses. International Journal for Numerical Methods in Engineering 1997; 40:2109-2127.
6. Graham E, Forsyth PA. Preconditioning methods for very ill-conditioned three-dimensional linear elasticity problems. International Journal for Numerical Methods in Engineering 1999; 44:77-99.
7. Saint-George P, Warzee G, Beauwens R, Notay Y. High-performance PCG solvers for FEM structural analysis. International Journal for Numerical Methods in Engineering 1996; 39:1313-1340.
8. Cai Z, Manteuffel TA, McCormick SF, Parter SV. First-order system least squares (FOSLS) for planar linear elasticity: pure traction problem. SIAM Journal on Numerical Analysis 1997; 35:320-335.
9. Augarde CE, Ramage A, Staudacher J. Element-based preconditioners for elasto-plastic problems in geotechnical engineering. International Journal for Numerical Methods in Engineering 2007; 71:757-779.
10. Meijerink JA, van der Vorst HA. An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Journal of Mathematical Computing 1977; 31:148-162.
11. Kershaw DS. The incomplete Cholesky-Conjugate Gradient method for the iterative solution of systems of linear equations. Journal of Computational Physics 1978; 20:43-65.
12. Saad Y. ILUT: a dual threshold incomlete LU factorization. Numerical Linear Algebra with Applications 1994; 1:387-402.
13. Benzi M. Preconditioning techniques for large linear systems: a survey. Journal of Computational Physics 2002; 182:418-477.
14. Gambolati G, Pini G, Ferronato M. Scaling improves stability of preconditioned CG-like solvers for FE consolidation equations. International Journal for Numerical and Analytical Methods in Geomechanics 2003; 27:1043-1056.
15. Chan SH, Phoon KK, Lee FH. A modified Jacobi preconditioner for solving ill-conditioned Biot's consolidation equations using symmetric quasi-minimal residual method. International Journal for Numerical and Analytical Method in Geomechanics 2001; 25:1001-1025.
16. Phoon KK, Toh KC, Chan SH, Lee FH. An efficient diagonal preconditioner for finite element solution of Biot's consolidation equations. International Journal for Numerical Methods in Engineering 2002; 55:377-400.
17. Chen X, Toh KC, Phoon KK. A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations. International Journal for Numerical Methods in Engineering 2006; 65:785-807.
18. Keller C, Gould NIM, Wathen AJ. Constraint preconditioning for indefinite linear systems. SIAM Journal on Matrix Analysis and Applications 2000; 21:1300-1317.
19. Silvester DJ, Elman HC, Kay D, Wathen AJ. Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow. Journal of Computational and Applied Mathematics 2001; 128:261-279.
20. Toh KC, Phoon KK, Chan SH. Block preconditioners for symmetric indefinite linear systems. International Journal for Numerical Methods in Engineering 2004; 60:1361-1381.
21. Bergamaschi L, Ferronato M, Gambolati G. Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations. Computer Methods in Applied Mechanics and Engineering 2007; 196:2647-2656.
22. Ferronato M, Pini G, Gambolati G. The role of preconditioning in the solution to FE coupled consolidation equations by Krylov subspace methods. International Journal for Numerical and Analytical Methods in Geomechanics 2009; 33:405-423.
23. Washio T, Hishada T, Watanabe W, Tezduyar H. A robust preconditioner for fluid-structure interaction problems. Computer Methods in Applied Mechanics and Engineering 2005; 194:4027-4047.
24. Ferronato M, Janna C, Gambolati G. Mixed constraint preconditioning in computational contact mechanics. Computer Methods in Applied Mechanics and Engineering 2008; 197:3922-3931.
25. Bergamaschi L, Ferronato M, Gambolati G. Mixed constraint preconditioners for the iterative solution of FE coupled consolidation equations. Journal of Computational Physics 2008; 227:9885-9897.
26. Bank RE, Wagner C. Multilevel ILU decomposition. Numerische Mathematik 1999; 82:543-576.
27. Meurant G. A multilevel AINV preconditioner. Numerical Algorithms 2002; 29:107-129.
28. Kraus JK. Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Numerical Linear Algebra with Applications 2006; 13:49-70.
29. Janna C, Ferronato M, Gambolati G. Multilevel incomplete factorizations for the iterative solution of non-linear finite element problems. International Journal for Numerical Methods in Engineering 2009; 80:651-670.
30. Ferronato M, Gambolati G, Teatini P. Ill-conditioning of finite element poroelasticity equations. International Journal of Solids and Structures 2001; 38:5995-6014.
31. Booker JR, Small JC. An investigation of the stability of numerical solutions of Biot's equations of consolidation. International Journal of Solids and Structures 1975; 11:907-917.
32. Ferronato M, Gambolati G, Janna C, Teatini P. Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs. International Journal for Numerical and Analytical Methods in Geomechanics 2008; 32:633-657.
33. Dostal Z. Inexact semi-monotonic Augmented Lagrangians with optimal feasibility convergence for quadratic programming with simple bounds and equality constraints. SIAM Journal on Numerical Analysis 2007; 45:500-513.
34. Janna C, Comerlati A, Gambolati G. A comparison of projective and direct solvers for Finite Elements in elastostatics. Advances in Engineering Software 2009; 40:675-685.
35. Gambolati G, Pini G, Ferronato M. Numerical performance of projection methods in finite element consolidation models. International Journal for Numerical and Analytical Methods in Geomechanics 2001; 25:1429-1447.
36. Gambolati G, Pini G, Ferronato M. Direct, partitioned and projected solution to finite element consolidation models. International Journal for Numerical and Analytical Methods in Geomechanics 2002; 26:1371-1383.
37. Curtis AR, Reid JK. On the automatic scaling of matrices for Gaussian elimination. Journal of the Institute of Mathematics and its Applications 1972; 10:118-124.
38. Benzi M, Cullum J, Tůma M. Robust approximate inverse preconditioning for the conjugate gradient method. SIAM Journal on Scientific Computing 2000; 22:1318-1332.
39. Ferronato M, Bergamaschi L, Gambolati G. Performance and robustness of block constraint preconditioners in Finite Element coupled consolidation problems. International Journal for Numerical Methods in Engineering 2010; 81:381-402.
40. Ferronato M, Gambolati G, Janna C. Efficient block preconditioners for the numerical modelling of geological faults. In Proceedings of the 12th International Conference of the International Association of Computer Methods and Advances in Geomechanics, Goa, India, Singh DN (ed.). 2008; 244-250. CD-ROM.
41. 2 sequestration in exploited gas fields. In Poromechanics IV, Ling HI et al. (eds). DEStech Publication: Lancaster, PA, 2009; 171-176.
42. Baù D, Ferronato M, Gambolati G, Teatini P. Basin scale compressibility of the Northern Adriatic by the radioactive marker technique. Geotechnique 2002; 52:605-616.