Shifted FSAI preconditioners for the efficient parallel solution of non-linear groundwater flow models

International Journal for Numerical Methods in Engineering

Volumn 89, Issue 13, 2012, Pages 1707-1719

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

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Approximate inverse; Groundwater flow models; Non linearity; Parallel preconditioning

Indexed keywords

APPROXIMATE INVERSE; COEFFICIENT MATRIX; COMPUTATIONAL GAINS; FINITE-ELEMENT DISCRETIZATION; GROUNDWATER FLOW MODEL; GROUNDWATER FLOW MODELS; ITERATIVE SOLUTIONS; NON-LINEARITY; NUMERICAL RESULTS; PARALLEL EFFICIENCY; PARALLEL PRECONDITIONING; PARALLEL SIMULATIONS; PARALLEL SOLUTIONS; PRECONDITIONERS; SHIFT STRATEGY; SPARSE APPROXIMATE INVERSE; STOCHASTIC DISTRIBUTION;

ALGORITHMS; AQUIFERS; COMPUTATIONAL EFFICIENCY; COMPUTER SIMULATION; GROUNDWATER FLOW; LINEAR SYSTEMS;

RADAR ANTENNAS;

EID: 84857500034     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3309     Document Type: Article

References (37)

1. Dagan G. Flow and Transport in Porous Formations. Springer-Verlag: Berlin, 1989.
2. Gelhar LW. Stochastic Subsurface Hydrology. Prentice-Hall: New Jersey, 1993.
3. Saad Y.ILUT: a dual threshold incomplete ILU factorization. Numerical Linear Algebra with Applications. 1994; 1:387-402.
4. Saad Y.1992.ILUM: A parallel multielimination ILU preconditioner for general sparse matrices. Technical Report CS-92-241, Department of Computer Science, University of Minnesota.
5. Karypis G, Kumar V. Parallel threshold-based ILU factorization. Proceedings of the 1997 ACM/IEEE Conference on Supercomputing, 1997; 1-28.
6. Dubois PF, Greenbaum A, Rodrigue GH. Approximating the inverse of a matrix for use in iterative algorithms on vector processors. Computing. 1979; 22:257-268.
7. Johnson OG, Micchelli CA, Paul G. Polynomial preconditioning for conjugate gradient calculations. SIAM Journal on Numerical Analysis. 1983; 20:362-376.
8. Axelsson O.A survey of preconditioned iterative methods for linear systems of algebraic equations. BIT. 1985; 25:166-187.
9. Benzi M, Tůma M.A comparative study of sparse approximate inverse preconditioners. Applied Numerical Mathematics. 1999; 30:305-340.
10. Kolotilina LY, Yeremin AY. Factorized sparse approximate inverse preconditioning. I. Theory. SIAM Journal on Matrix Analysis and Applications. 1993; 14:45-58.
11. Bergamaschi L, Pini G, Sartoretto F. Parallel eigenanalysis of multiaquifer systems. International Journal for Numerical Methods in Engineering. 2005; 63:2069-2085.
12. Bergamaschi L, Martinez A, Pini G. Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems. Applied Mathematics and Computation. 2006; 175:1694-1715.
13. Meurant G. On the incomplete Cholesky decomposition of a class of perturbed matrices. SIAM Journal on Scientific Computing. 2001; 23:419-429.
14. Benzi M, Bertaccini D. Approximate inverse preconditioning for shifted linear systems. BIT. 2003; 43:231-244.
15. Florez E, Garcia MD, Rodriguez-Jimenez E, Sarmiento H, Suarez A, Montero G.2008. Incomplete factorization for preconditioning shifted linear systems arising in wind modelling. In Proceedings of the Sixth International Conference on Engineering Computational Technology. Papadrakakis M, Topping BHV (eds). Civil-Comp Press: Stirlingshire, DOI: 10.4203/ccp.89.70, paper no. 70.
16. Bellavia S, De Simone V, Di Serafino D, Morini B. Efficient preconditioner updates for shifted linear systems. SIAM Journal on Scientific Computing. 2011; 33:1785-1809.
17. D'Haese CMF, Putti M, Paniconi C, Verhoest NEC. Assessment of adaptive and heuristic time stepping for variably saturated flow. International Journal for Numerical Methods in Fluids. 2007; 53:1173-1193.
18. Teatini P, Baù D, Gambolati G. Water-gas dynamics and coastal land subsidence over Chioggia Mare field, northern Adriatic Sea. Hydrogeology Journal. 2000; 8:462-479.
19. Gambolati G, Teatini P, Tomasi L. Stress/strain analysis in productive gas/oil reservoirs. International Journal for Numerical and Analytical Methods in Geomechanics. 1999; 23:1495-1519.
20. 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.
21. Hueckel T, Cassiani G, Prevost JH, Walters DA.2005. Field derived compressibility of deep sediments of the Northern Adriatic. In Land Subsidence-Special Volume, Proceedings of the Seventh International Symposium on Land Subsidence. Millpress Science Publishers, Rotterdam; 35-49.
22. Ferronato M, Gambolati G, Teatini P, Baù D. Stochastic poromechanical modeling of anthropogenic land subsidence. International Journal of Solids and Structures. 2006; 43:3324-3336.
23. Grote M, Huckle T. Parallel preconditioning with sparse approximate inverses. SIAM Journal on Scientific Computing. 1997; 18:838-853.
24. Chow E, Saad Y. Approximate inverse preconditioners via sparse-sparse iterations. SIAM Journal on Scientific Computing. 1998; 19:995-1023.
25. Benzi M, Cullum J, Tůma M. Robust approximate inverse preconditioning for the conjugate gradient method. SIAM Journal on Scientific Computing. 2000; 22:1318-1332.
26. Saad Y. Iterative Methods for Sparse Linear Systems. PWS Publishing Company: Boston, 1996.
27. Benzi M, Tůma M.A parallel solver for large-scale Markov chains. Applied Numerical Mathematics. 2002; 41:135-153.
28. Kolotilina LY, Yeremin AY. Factorized sparse approximate inverse preconditioning. II. Solution of 3D FE systems on massively parallel computers. International Journal of High Speed Computing. 1995; 7:191-215.
29. Bergamaschi L, Pini G, Sartoretto F. Approximate inverse preconditioning in the parallel solution of sparse eigenproblems. Numerical Linear Algebra with Applications. 2000; 7:99-116.
30. Bergamaschi L, Gambolati G, Pini G.A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations. Journal of Computational and Applied Mathematics. 2007; 210:64-70.
31. Kolotilina LY, Yeremin AY. Factorized sparse approximate inverse preconditioning. IV. Simple approaches to rising efficiency. Numerical Linear Algebra with Applications. 1999; 6:515-531.
32. Anderson G, Bai Z, Bischof C, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Kenney AM, Ostrouchov S, Sorensen D. LAPACK User's Guide. SIAM: Philadelphia, 1992.
33. Pacheco PS. Parallel Programming with MPI. Morgan Kaufmann Publ: San Francisco, 1997.
34. Bergamaschi L, Putti M. Efficient parallelization of preconditioned conjugate gradient schemes for matrices arising from the discretizations of diffusion equations. Proceedings of the 9th SIAM Conference on Parallel Processing for Scientific Computing, 1999.
35. Teatini P, Ferronato M, Gambolati G, Baù D, Putti M. Anthropogenic Venice uplift by seawater pumping into a heterogeneous aquifer system. Water Resources Research. 2010; 46(W11547). DOI: 10.1029/2010WR009161.
36. Cuthill E, McKee J. Reducing the bandwidth of sparse symmetric matrices. Proceedings of the 1969 24th National Conference, 1969; 157-172.
37. Li Z, Saad Y, Sosonkina M.pARMS: a parallel version of the algebraic recursive multilevel solver. Numerical Linear Algebra with Applications. 2003; 10:485-509.