A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries

Journal of Computational Physics

Volumn 230, Issue 12, 2011, Pages 4756-4771

  Guillet, Thomas ^a   Teyssier, Romain ^a,b  

^a CEA SACLAY   (France)

^b UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Adaptive mesh refinement; Elliptic methods; Multigrid methods; Poisson equation

Indexed keywords

ACCELERATION; BOUNDARY CONDITIONS; INDIUM COMPOUNDS; MEMORY ARCHITECTURE; MESH GENERATION; NUMERICAL ANALYSIS;

ADAPTIVE MESH REFINEMENT; ADAPTIVE MESH REFINEMENT SCHEMES; CARTESIAN GRID; DIRICHLET BOUNDARY CONDITION; DOMAIN BOUNDARY; ELLIPTIC METHODS; IRREGULAR DOMAINS; MULTIGRID METHODS; MULTIGRIDS; SIMPLE++;

POISSON EQUATION;

EID: 79955673560     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.02.044     Document Type: Article

References (32)

1. Almgren A., Bell J., Colella P., Marthaler T. A cartesian grid projection method for the incompressible euler equations in complex geometries. SIAM Journal of Scientific Computing 1997, 18:1289-1309.
2. Brandt A. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 1977, 31:333-390.
3. Brandt A., Mikulinsky V. On recombining iterants in multigrid algorithms and problems with small islands. SIAM Journal of Scientific Computing 1995, 16(1):20-28.
4. Cheng H., Greengard L., Rokhlin V. A fast adaptive multipole algorithm in three dimensions. Journal of Computational Physics 1999, 155:468-498.
5. Colella P., Woodward P.R. The piecewise parabolic method (PPM) for gas-dynamical simulations. Journal of Computational Physics 1984, 54(Sep.):174-201.
6. M.S. Day, P. Colella, M.J. Lijewski, C.A. Rendleman, D.L. Marcus, Embedded boundary algorithms for solving the Poisson equation on complex domains. Technical Report LBNL-41811, Lawrence Berkeley National Laboratory, 1998 (May).
7. Gibou F., Fedkiw R.P., Cheng L.-T., Kang M. A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. Journal of Computational Physics 2002, 176(Feb.):205-227.
8. Huang J., Greengard L. A fast direct solver for elliptic partial differential equations on adaptively refined meshes. SIAM Journal of Scientific Computing 2000, 21.
9. Jessop C., Duncan M., Chau W.Y. Multigrid methods for N-body gravitational systems. Journal of Computational Physics 1994, 115(Dec.):339-351.
10. Johansen H., Colella P. A cartesian grid embedded boundary method for Poisson's equation on irregular domains. Journal of Computational Physics 1998, 147(1):60-85.
11. Khokhlov A. Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations. Journal of Computational Physics 1998, 143(July):519-543.
12. Knebe A., Gibson B.K. Galactic haloes in MONDian cosmological simulations. MNRAS 2004, 347(Feb.):1055-1064.
13. Kravtsov A.V., Klypin A.A., Khokhlov A.M. Adaptive refinement tree: a new high-resolution N-body code for cosmological simulations. ApJS 1997, 111(July):73. +.
14. Liu X., Fedkiw R.P., Kang M. A boundary condition capturing method for Poisson's equation on irregular domains. Journal of Computational Physics 2000, 160(May):151-178.
15. Llinares C., Zhao H.S., Knebe A. Physics of galactic colliders: high-speed satellites in ΛCDM versus Mondian cosmology. ApJ 2009, 695(Apr.):L145-L148.
16. D. Martin, K. Cartwright, Solving Poisson's Equation Using Adaptive Mesh Refinement, Technical Report, UCB/ERL M96/66, U.C. Berkeley, 1996.
17. Martin D., Colella P. A cell-centered adaptive projection method for the incompressible euler equations. Journal of Computational Physics 2000, 163:271-312.
18. McCorquodale P., Colella P., Johansen H. A cartesian grid embedded boundary method for the heat equation on irregular domains. Journal of Computational Physics 2001, 173(2):620-635.
19. Miniati F., Colella P. Block structured adaptive mesh and time refinement for hybrid, hyperbolic+N-body systems. Journal of Computational Physics 2007, 227(Nov.):400-430.
20. Osher S., Fedkiw R.P. Level set methods: an overview and some recent results. Journal of Computational Physics 2001, 169(May):463-502.
21. Popinet S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. Journal of Computational Physics 2003, 190(Sep.):572-600.
22. Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. Numerical Recipes in C: The Art of Scientific Computing 1992, Cambridge University Press.
23. Ricker P.M. A direct multigrid Poisson solver for oct-tree adaptive meshes. ApJS 2008, 176(May):293-300.
24. Rudman M. A volume-tracking method for incompressible multifluid flows with large density variations. International Journal for Numerical Methods in Fluids 1998, 28(Aug.):357-378.
25. Saad Y. Iterative methods for sparse linear systems 2003, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
26. Sussman M., Almgren A.S., Bell J.B., Colella P., Howell L.H., Welcome M.L. An adaptive level set approach for incompressible two-phase flows. Journal of Computational Physics 1999, 148(Jan.):81-124.
27. Sussman M., Smereka P., Osher S. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics 1994, 114(Sep.):146-159.
28. Teyssier R. Cosmological hydrodynamics with adaptive mesh refinement. A new high resolution code called RAMSES. A&A 2002, 385(Apr.):337-364.
29. Tiret O., Combes F. Evolution of spiral galaxies in modified gravity. A&A 2007, 464(Mar.):517-528.
30. van Leer B. On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe. SIAM Journal on Scientific and Statistical Computing 1984, 5(1):1-20.
31. Wesseling P. An Introduction to Multigrid Methods 1992, Wiley.
32. Ye T., Mittal R., Udaykumar H.S., Shyy W. An accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries. Journal of Computational Physics 1999, 156:209-240.