A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system

Numerical Linear Algebra with Applications

Volumn 11, Issue 2-3, 2004, Pages 93-113

  Gaspar, F J ^a   Lisbona, F J ^a   Oosterlee, C W ^b   Wienands, R ^c  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c FRAUNHOFER INSTITUTE FOR ALGORITHMS AND SCIENTIFIC COMPUTING SCAI   (Germany)

Author keywords

Comparison; Coupled relaxation; Decoupled distributive relaxation; Multigrid; Poroelasticity; Staggered discretization

Indexed keywords

EID: 10044270001     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.372     Document Type: Article

References (23)

1. Brandt A, Dinar N. Multigrid solutions to elliptic flow problems. In Parter S (ed.). Numerical Methods for Partial Differential Equations. Academic Press: New York, 1979; 53-147.
2. Vanka SP. Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. Journal of Computational Physics 1986; 65:138-158.
3. Gaspar FJ, Lisbona FJ, Oosterlee CW, Wienands R. An Efficient Multigrid Solver Based on Distributive Smoothing for Poroelasticity Equations, submitted for publication.
4. Sivaloganathan S. The use of local mode analysis in the design and comparison of multigrid methods. Computer Physics Communications 1991; 65:246-252.
5. Sockol P. Multigrid solution of the Navier-Stokes equations on highly stretched grids. International Journal for Numerical Methods in Fluids 1993; 17:543-566.
6. Paisley MF, Bhatti NM. Comparison of multigrid methods for neutral and stably stratified flows over twodimensional obstacles. Journal of Computational Physics 1998; 142:581-610.
7. Wesseling P, Oosterlee CW. Geometric multigrid with applications to computational fluid dynamics. Journal of Computational and Applied Mathematics 2001; 128:311-334.
8. Osorio JG, Chen H-Y, Teufel LW. Numerical simulation of the impact of flow-induced geomechanical response on the productivity of stress-sensitive reservoirs. Society of Petroleum Engineers SPE 1999; 51929:1-15.
9. Brandt A, Yavneh I. On multigrid solution of high-Reynolds incompressible entering flows. Journal of Computational Physics 1992; 101:151-164.
10. Ruge JW, Stüben K. Algebraic multigrid (AMG). In Multigrid Methods, Frontiers in Applied Math, Me Cormick SF (ed.). SIAM: Philadelphia, 1987; 73-130.
11. Biot MA. General theory of three dimensional consolidation. Journal of Applied Physics 1941; 12:155-164.
12. Gaspar FJ, Lisbona FJ, Vabishchevich PN. A finite difference analysis of Biot's consolidation model. Applied Numerical Mathematics 2003; 44:487-506.
13. Harlow FH, Welch JE. Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Physics of Fluids 1965; 8:2182-2189.
14. Wesseling P. Principles of Computational Fluid Dynamics. Springer: Berlin, 2001.
15. Wittum G. Multi-grid methods for Stokes and Navier-Stokes equations with transforming smoothers: algorithms and numerical results. Numerische Mathematik 1999; 54:543-563.
16. Brandt A. Multigrid Techniques. 1984 Guide with Applications to Fluid Dynamics, GMD-Studie No. 85. Sankt Augustin: Germany, 1984.
17. Stüben K, Trottenberg U. Multigrid methods: fundamental algorithms, model problem analysis and applications. In Multigrid Methods, Lecture Notes in Mathematics, Hackbusch W, Trottenberg U (eds), vol. 960. Springer: Berlin, 1982; 1-176.
18. Trottenberg U, Oosterlee CW, Schüller A. Multigrid. Academic Press: New York, 2001.
19. Wienands R. Extended local fourier analysis for multigrid: optimal smoothing, coarse grid correction and preconditioning. Ph.D. Thesis, University of Cologne, Germany, 2001.
20. Livne OE, Brandt A. Local mode analysis of multicolour and composite relaxation schemes. Computers and Mathematics with Applications, 2003; 47:301-317.
21. Oosterlee CW, Wesseling P. A robust multigrid method for a discretization of the incompressible Navier-Stokes equations in general coordinates. Impact of Computers in Science and Engineering 1993; 5:128-151.
22. Thompson MC, Ferziger JH. An adaptive multigrid technique for the incompressible Navier-Stokes equations. Journal of Computational Physics 1989; 82:94-121.
23. Barry SI, Mercer GN. Exact solutions for 2D time dependent flow and deformation within a poroelastic medium. Journal of Applied Mechanics (ASME) 1999; 66:536-540.