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The Impact of AMR in Numerical Astrophysics and Cosmology

  • Michael L. Norman
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 41)

Abstract

I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell refinement, and patch refinement, otherwise known as block-structured adaptive mesh refinement (SAMR). In this survey, no attempt is made to assess the relative merits of these two approaches. Rather, the discussion focuses on how AMR is being used and how AMR is making a scientific impact in a diverse set of fields from space physics to the cosmology of the early universe. The increased adoption of AMR techniques in the past decade is driven in part by the public availability of AMR codes and frameworks. I provide a partial list of resources for those interested in learning more about AMR simulations.

Keywords

White Dwarf Adaptive Mesh Radiative Shock Piecewise Parabolic Method Molecular Cloud Core 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    M. J. Berger and J. Oliger. Adaptive mesh refinement for hyperbolic partial differential equations. J. Comp. Phys., 53:484–512, 1984.MathSciNetCrossRefGoogle Scholar
  2. 2.
    P. R. Woodward and P. Colella. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comp. Physics, 54:115–173, 1984.MathSciNetCrossRefGoogle Scholar
  3. 3.
    M. J. Berger and P. Colella. Local adaptive mesh refinement for shock hydrodynamics. J. Comp. Phys., 82:64–84, 1989.CrossRefGoogle Scholar
  4. 4.
    D. De Zeeuw. Amr method for mhd. SIAM J. Sci. Comp., 20:22, 1998.Google Scholar
  5. 5.
    C. P. T. Groth, D. L. de Zeeuw, T. I. Gombosi, and K. G. Powell. A Parallel Adaptive 3D MHD Scheme for Modeling Coronal and Solar Wind Plasma Flows. Space Science Reviews, 87:193–198, 1999.CrossRefGoogle Scholar
  6. 6.
    C. P. T. Groth, D. L. de Zeeuw, T. I. Gombosi, and K. G. Powell. Global threedimensional MHD simulation of a space weather event: CME formation, interplanetary propagation, and interaction with the magnetosphere. J. Geophys. Res., 105:25053–25078, November 2000.CrossRefGoogle Scholar
  7. 7.
    S. A. E. G. Falle and A. C. Raga. The structure of knots in variable stellar jets. I-Symmetric knots. MNRAS, 261:573–583, April 1993.Google Scholar
  8. 8.
    S. A. E. G. Falle and A. C. Raga. The structure of knots in variable stellar jets-II. Asymmetric knots. MNRAS, 272:785–799, February 1995.Google Scholar
  9. 9.
    R. I. Klein, C. F. McKee, and P. Colella. On the hydrodynamic interaction of shock waves with interstellar clouds. 1: Nonradiative shocks in small clouds. ApJ, 420:213–236, January 1994.CrossRefGoogle Scholar
  10. 10.
    R. I. Klein, K. Truelove, and C. F. McKee. The Jeans Condition: A New Constraint on Spatial Resolution in Simulations of Self-Gravitational Hydrodynamics. In ASP Conf. Ser. 123: Computational Astrophysics; 12th Kingston Meeting on Theoretical Astrophysics, pages 152-+, 1997.Google Scholar
  11. 11.
    R. I. Klein, R. T. Fisher, M. R. Krumholz, and C. F. McKee. Recent Advances in the Collapse and Fragmentation of Turbulent Molecular Cloud Cores. In Revista Mexicana de Astronomia y Astrofisica Conference Series, pages 92–96, January 2003.Google Scholar
  12. 12.
    J. K. Truelove, R. I. Klein, C. F. McKee, J. H. Holliman, L. H. Howell, and J. A. Greenough. The Jeans Condition: A New Constraint on Spatial Resolution in Simulations of Isothermal Self-gravitational Hydrodynamics. ApJLett, 489:L179+, November 1997.CrossRefGoogle Scholar
  13. 13.
    J. K. Truelove, R. I. Klein, C. F. McKee, J. H. Holliman, L. H. Howell, J. A. Greenough, and D. T. Woods. Self-gravitational Hydrodynamics with Three-dimensional Adaptive Mesh Refinement: Methodology and Applications to Molecular Cloud Collapse and Fragmentation. ApJ, 495:821-+, March 1998.CrossRefGoogle Scholar
  14. 14.
    A. M. Khokhlov. Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations. J. Comp. Phys., 143:519–543, 1998.zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    A. Kritsuk, T. Plewa, and E. Müller. Convective cores in galactic cooling flows. MNRAS, 326:11–22, September 2001.CrossRefGoogle Scholar
  16. 16.
    S. A. E. G. Falle, R. F. Coker, J. M. Pittard, J. E. Dyson, and T. W. Hartquist. numerical simulations of tail formation in wind interactions with injected material. MNRAS, 329:670–674, January 2002.CrossRefGoogle Scholar
  17. 17.
    A. C. Calder, B. Fryxell, T. Plewa, R. Rosner, L. J. Dursi, V. G. Weirs, T. Dupont, H. F. Robey, J. O. Kane, B. A. Remington, R. P. Drake, G. Dimonte, M. Zingale, F. X. Timmes, K. Olson, P. Ricker, P. MacNeice, and H. M. Tufo. On Validating an Astrophysical Simulation Code. ApJSupp, 143:201–229, November 2002.CrossRefGoogle Scholar
  18. 18.
    G. L. Bryan and M. L. Norman. In D. A. Clarke and M. Fall, editors, Computational Astrophysics; 12th Kingston Meeting on Theoretical Astrophysics, proceedings of meeting held in Halifax; Nova Scotia; Canada October 17–19; 1996. ASP Conference Series # 123, 1997.Google Scholar
  19. 19.
    G. L. Bryan and M. L. Norman. A hybrid amr application for cosmology and astrophysics. In N. Chrisochoides, editor, Workshop on Structured Adaptive Mesh Refinement Grid Methods, page 165. IMA Volumes in Mathematics No. 117, 2000.Google Scholar
  20. 20.
    A. V. Kravtsov, A. A. Klypin, and A. M. Khokhlov. Adaptive Refinement Tree: A New High-Resolution N-Body Code for Cosmological Simulations. ApJSupp, 111:73-+, July 1997.CrossRefGoogle Scholar
  21. 21.
    A. Klypin, S. Gottlöber, A. V. Kravtsov, and A. M. Khokhlov. Galaxies in N-Body Simulations: Overcoming the Overmerging Problem. ApJ, 516:530–551, May 1999.CrossRefGoogle Scholar
  22. 22.
    T. Abel, G. L. Bryan, and M. L. Norman. The Formation and Fragmentation of Primordial Molecular Clouds. ApJ, 540:39–44, September 2000.CrossRefGoogle Scholar
  23. 23.
    T. Abel, G. L. Bryan, and M. L. Norman. The Formation of the First Star in the Universe. Science, 295:93–98, January 2002.CrossRefGoogle Scholar
  24. 24.
    C. Loken, M. L. Norman, E. Nelson, J. Burns, G. L. Bryan, and P. Motl. A Universal Temperature Profile for Galaxy Clusters. ApJ, 579:571–576, November 2002.CrossRefGoogle Scholar
  25. 25.
    K. Tassis, T. Abel, G. L. Bryan, and M. L. Norman. Numerical Simulations of High-Redshift Star Formation in Dwarf Galaxies. ApJ, 587:13–24, April 2003.CrossRefGoogle Scholar
  26. 26.
    D. Nagai, A. V. Kravtsov, and A. Kosowsky. Effect of Internal Flows on Sunyaev-Zeldovich Measurements of Cluster Peculiar Velocities. ApJ, 587:524–532, April 2003.CrossRefGoogle Scholar
  27. 27.
    H. M. P. Couchman. Mesh-refined P3M-A fast adaptive N-body algorithm. ApJL, 368:L23–L26, February 1991.CrossRefGoogle Scholar
  28. 28.
    G. L. Bryan. Fluids in the universe: Adaptive mesh in cosmology. Computing in Science and Engineering, 1:2:46, 1999.MathSciNetCrossRefGoogle Scholar
  29. 29.
    K. Kifonidis, T. Plewa, H.-T. Janka, and E. Müller. Nucleosynthesis and Clump Formation in a Core-Collapse Supernova. ApJLett, 531: L123–L126, March 2000CrossRefGoogle Scholar
  30. 30.
    F. X. Timmes, M. Zingale, K. Olson, B. Fryxell, P. Ricker, A. C. Calder, L. J. Dursi, H. Tufo, P. MacNeice, J. W. Truran, and R. Rosner. On the Cellular Structure of Carbon Detonations. ApJ, 543:938–954, November 2000.CrossRefGoogle Scholar
  31. 31.
    V. N. Gamezo, A. M. Khokhlov, E. S. Oran, A. Y. Chtchelkanova, and R. O. Rosenberg. Thermonuclear Supernovae: Simulations of the Deflagration Stage and Their Implications. Science, 299:77–81, January 2003.CrossRefGoogle Scholar
  32. 32.
    R. Cid-Fernandes, T. Plewa, M. Rozyczka, J. Franco, R. Terlevich, G. Tenorio-Tagle, and W. Miller. On the evolution of ejecta fragments in compact supernova remnants. MNRAS, 283:419–430, November 1996.Google Scholar
  33. 33.
    D. Balsara. Adaptive Mesh Refinement in Computational Astrophysics — Methods and Applications. Journal of Korean Astronomical Society, 34:181–190, December 2001.Google Scholar
  34. 34.
    A. J. Mioduszewski, P. A. Hughes, and G. C. Duncan. Simulated VLBI Images from Relativistic Hydrodynamic Jet Models. ApJ, 476:649-+, February 1997.CrossRefGoogle Scholar
  35. 35.
    S. S. Komissarov and S. A. E. G. Falle. Simulations of Superluminal Radio Sources. MNRAS, 288:833–848, July 1997.Google Scholar
  36. 36.
    K. Powell. ICASE Report, 94–24, 1994.Google Scholar
  37. 37.
    K. Powell et al. AIAA Paper, 95-1704-CP, 1995.Google Scholar
  38. 38.
    P. M. Roe. Approximate riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys., 43:357, 1981.zbMATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    A. Harten, P. Lax, and B. Van Leer. On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Rev., 25:1:35–61, 1983.MathSciNetCrossRefGoogle Scholar
  40. 40.
    A. M. Khokhlov. Propagation of Turbulent Flames in Supernovae. ApJ, 449:695-+, August 1995.CrossRefGoogle Scholar
  41. 41.
    M. Herant, W. Benz, W. R. Hix, C. L. Fryer, and S. A. Colgate. Inside the supernova: A powerful convective engine. ApJ, 435:339–361, November 1994.CrossRefGoogle Scholar
  42. 42.
    M. Reinecke, W. Hillebrandt, and J. C. Niemeyer. Refined numerical models for multidimensional type Ia supernova simulations. A&A, 386:936–943, May 2002.CrossRefGoogle Scholar
  43. 43.
    D. Arnett and E. Livne. The delayed-detonation model of a type IA supernovae. 1: The deflagration phase. ApJ, 427:315–329, May 1994.CrossRefGoogle Scholar
  44. 44.
    P. Hoflich, A. M. Khokhlov, and J. C. Wheeler. Delayed detonation models for normal and subluminous type IA sueprnovae: Absolute brightness, light curves, and molecule formation. ApJ, 444:831–847, May 1995.CrossRefGoogle Scholar
  45. 45.
    A. M. Khokhlov and E. Oran. Combust. Flame, 1999.Google Scholar
  46. 46.
    B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb, P. MacNeice, R. Rosner, J.W. Truran, and H. Tufo. FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes. ApJSupp, 131:273–334, November 2000.CrossRefGoogle Scholar
  47. 47.
    A. M. Khokhlov. Delayed detonation model for type IA supernovae. A&A, 245:114–128, May 1991.Google Scholar
  48. 48.
    M. Zingale, F. X. Timmes, B. Fryxell, D. Q. Lamb, K. Olson, A. C. Calder, L. J. Dursi, P. Ricker, R. Rosner, P. MacNeice, and H. M. Tufo. Helium Detonations on Neutron Stars. ApJSupp, 133:195–220, March 2001.CrossRefGoogle Scholar
  49. 49.
    S. E. Woosley, A. Heger, and T. A. Weaver. The evolution and explosion of massive stars. Reviews of Modern Physics, 74:1015–1071, November 2002.CrossRefGoogle Scholar
  50. 50.
    A. Burrows, J. Hayes, and B. A. Fryxell. On the Nature of Core-Collapse Supernova Explosions. ApJ, 450:830-+, September 1995.CrossRefGoogle Scholar
  51. 51.
    A. Mezzacappa and TeraScale Supernova Initiative Collaboration. TeraScale Supernova Initiative. Bulletin of the American Astronomical Society, 34:687-+, May 2002.Google Scholar
  52. 52.
    K. Kifonidis, T. Plewa, H.-T. Janka, and E. Müller. non-spherical core collapse supernovae. I. Neutrino-driven convection, Rayleigh-Taylor instabilities, and the formation and propagation of metal clumps. A&A, 408:621–649, September 2003.CrossRefGoogle Scholar
  53. 53.
    T. Plewa and E. Müller. The consistent multi-fluid advection method. A&A, 342:179–191, February 1999.Google Scholar
  54. 54.
    P. Colella and P. R. Woodward. The piecewise parabolic method (ppm) for gas-dynamical simulations. J. Comp. Physics, 54:174–201, 1984.MathSciNetCrossRefGoogle Scholar
  55. 55.
    A. Y. Poludnenko, A. Frank, and E. G. Blackman. Hydrodynamic Interaction of Strong Shocks with Inhomogeneous Media. I. Adiabatic Case. ApJ, 576:832–848, September 2002.CrossRefGoogle Scholar
  56. 56.
    M. J. Berger and R. LeVeque. Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems. SIAM J. Num. Anal., 35: 2298–2316, 1998.MathSciNetCrossRefGoogle Scholar
  57. 57.
    R. Walder and D. Folini. Knots, filaments, and turbulence in radiative shocks. A&A, 330:L21–L24, February 1998.Google Scholar
  58. 58.
    R. A. Chevalier and J. N. Imamura. Linear analysis of an oscillatory instability of radiative shock waves. ApJ, 261:543–549, October 1982.CrossRefGoogle Scholar
  59. 59.
    K.-H. A. Winkler and M. J. Newman. Formation of solar-type stars in spherical symmetry. I-The key role of the accretion shock. ApJ, 236: 201–211, February 1980.CrossRefGoogle Scholar
  60. 60.
    K.-H. A. Winkler and M. J. Newman. Formation of solar-type stars in spherical symmetry. II-Effects of detailed constitutive relations. ApJ, 238:311–325, May 1980.CrossRefGoogle Scholar
  61. 61.
    A. Burkert and P. Bodenheimer. Fragmentation in a centrally condensed protostar. MNRAS, 280:1190–1200, June 1996.Google Scholar
  62. 62.
    S. Inutsuka and S. M. Miyama. Self-similar solutions and the stability of collapsing isothermal filaments. ApJ, 388:392–399, April 1992.CrossRefGoogle Scholar
  63. 63.
    R. B. Larson. The physics of star formation. Rep. Prog. Phys., 66:1651–97, 2003.CrossRefGoogle Scholar
  64. 64.
    A. P. Boss, R. T. Fisher, R. I. Klein, and C. F. McKee. The Jeans Condition and Collapsing Molecular Cloud Cores: Filaments or Binaries? ApJ, 528:325–335, January 2000.CrossRefGoogle Scholar
  65. 65.
    L. H. Howell and J. A. Greenough. Radiation diffusion for multi-fluid eulerian hydrodynamics with adaptive mesh refinement. J. Comp. Phys., 184: 53–78, 2003.MathSciNetCrossRefGoogle Scholar
  66. 66.
    B. Reipurth and J. Bally. Herbig-Haro Flows: Probes of Early Stellar Evolution. Ann. Rev. Astron. Astrophys., 39:403–455, 2001.CrossRefGoogle Scholar
  67. 67.
    A. Ferrari. Modeling Extragalactic Jets. Ann. Rev. Astron. Astrophys., 36:539–598, 1998.CrossRefGoogle Scholar
  68. 68.
    M. J. Rees. The M87 jet-Internal shocks in a plasma beam. MNRAS, 184:61P–65P, September 1978.Google Scholar
  69. 69.
    A. C. Raga, L. Binette, J. Canto, and N. Calvet. Stellar jets with intrinsically variable sources. ApJ, 364:601–610, December 1990.CrossRefGoogle Scholar
  70. 70.
    S. A. E. G. Falle. The Effect of Turbulence on the Largescale Structure of Radio Jets. MNRAS, 269:607-+, August 1994.Google Scholar
  71. 71.
    R. D. Blandford and A. Konigl. Relativistic jets as compact radio sources. ApJ, 232:34–48, August 1979.CrossRefGoogle Scholar
  72. 72.
    G. C. Duncan and P. A. Hughes. Simulations of relativistic extragalactic jets. ApJLett, 436:L119+, December 1994.CrossRefGoogle Scholar
  73. 73.
    J. M. A. Marti, E. Muller, J. A. Font, and J. M. Ibanez. Morphology and Dynamics of Highly Supersonic Relativistic Jets. ApJLett, 448:L105+, August 1995.Google Scholar
  74. 74.
    P. E. Hardee, A. Rosen, P. A. Hughes, and G. C. Duncan. Time-dependent Structure of Perturbed Relativistic Jets. ApJ, 500:599-+, June 1998.CrossRefGoogle Scholar
  75. 75.
    A. Rosen, P. A. Hughes, G. C. Duncan, and P. E. Hardee. A Comparison of the Morphology and Stability of Relativistic and Nonrelativistic Jets. ApJ, 516:729–743, May 1999.CrossRefGoogle Scholar
  76. 76.
    J. J. Quirk. Adaptive mesh refinement for shockwave simulations. Ph.D. Thesis, 1991.Google Scholar
  77. 77.
    R. Hockney and J. Eastwood. In Computer Simulation Using Particles. McGraw Hill, New York, 1988.Google Scholar
  78. 78.
    C. Jessop, M. Duncan, and W. Y. Chau. Multigrid methods for n-body gravitational systems. J. Comp. Phys., 115:339–351, 1994.CrossRefGoogle Scholar
  79. 79.
    A. Knebe, A. Green, and J. Binney. Multi-level adaptive particle mesh (MLAPM): a c code for cosmological simulations. MNRAS, 325: 845–864, August 2001.CrossRefGoogle Scholar
  80. 80.
    B. Moore, N. Katz, and G. Lake. On the Destruction and Overmerging of Dark Halos in Dissipationless N-Body Simulations. ApJ, 457:455-+, February 1996.CrossRefGoogle Scholar
  81. 81.
    S. D. M. White. The dynamics of rich clusters of galaxies. MNRAS, 177:717–733, December 1976.Google Scholar
  82. 82.
    N. Katz, L. Hernquist, and D. H. Weinberg. Galaxies and gas in a cold dark matter universe. ApJLett, 399:L109–L112, November 1992.CrossRefGoogle Scholar
  83. 83.
    R. Cen. A hydrodynamic approach to cosmology-Methodology. ApJSupp, 78:341–364, February 1992.CrossRefGoogle Scholar
  84. 84.
    D. Ryu, J. P. Ostriker, H. Kang, and R. Cen. A cosmological hydrodynamic code based on the total variation diminishing scheme. ApJ, 414:1–19, September 1993.CrossRefGoogle Scholar
  85. 85.
    W. Y. Anninos and M. L. Norman. Nonlinear hydrodynamics of cosmological sheets. 1: Numerical techniques and tests. Astrophysical Journal, 429:434–464, July 1994.CrossRefGoogle Scholar
  86. 86.
    P. Anninos, M. L. Norman, and D. A. Clarke. Hierarchical numerical cosmology with hydrodynamics: Methods and code tests. ApJ, 436:11–22, November 1994.CrossRefGoogle Scholar
  87. 87.
    G. L. Bryan, M. L. Norman, J. M. Stone, R. Cen, and J. P. Ostriker. A piecewise parabolic method for cosmological hydrodynamics. Comp. Phys. Comm., 89:149–168, 1995.CrossRefGoogle Scholar
  88. 88.
    P. M. Ricker, S. Dodelson, and D. Q. Lamb. COSMOS: A Hybrid N-Body/ Hydrodynamics Code for Cosmological Problems. ApJ, 536:122–143, June 2000.CrossRefGoogle Scholar
  89. 89.
    Y. Zhang, P. Anninos, and M. L. Norman. A Multispecies Model for Hydrogen and Helium Absorbers in Lyman-Alpha Forest Clouds. ApJLett, 453:L57+, November 1995.Google Scholar
  90. 90.
    A. V. Kravtsov. High-resolution simulations of structure formation in the universe. Ph.D. Thesis, 1999.Google Scholar
  91. 91.
    R. Teyssier. Cosmological hydrodynamics with adaptive mesh refinement. A new high resolution code called RAMSES. A&A, 385:337–364, April 2002.CrossRefGoogle Scholar
  92. 92.
    P. Anninos, Y. Zhang, T. Abel, and M. L. Norman. Cosmological hydrodynamics with multi-species chemistry and nonequilibrium ionization and cooling. New Astronomy, 2:209–224, August 1997.CrossRefGoogle Scholar
  93. 93.
    C. S. Frenk, S. D. M. White, P. Bode, J. R. Bond, G. L. Bryan, R. Cen, H. M. P. Couchman, A. E. Evrard, N. Gnedin, A. Jenkins, A. M. Khokhlov, A. Klypin, J. F. Navarro, M. L. Norman, J. P. Ostriker, J. M. Owen, F. R. Pearce, U.-L. Pen, M. Steinmetz, P. A. Thomas, J. V. Villumsen, J. W. Wadsley, M. S. Warren, G. Xu, and G. Yepes. The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions. ApJ, 525:554–582, November 1999.CrossRefGoogle Scholar
  94. 94.
    A. V. Kravtsov, A. Klypin, and Y. Hoffman. Constrained Simulations of the Real Universe. II. Observational Signatures of Intergalactic Gas in the Local Supercluster Region. ApJ, 571:563–575, June 2002.CrossRefGoogle Scholar
  95. 95.
    A. Refregier and R. Teyssier. Numerical and analytical predictions for the large-scale Sunyaev-Zel’dovich effect. Phys. Rev. D, 66:043002-+, August 2002.CrossRefGoogle Scholar
  96. 96.
    J. Silk. The first stars. MNRAS, 205:705–718, November 1983.Google Scholar
  97. 97.
    G. L. Bryan, T. Abel, and M. L. Norman. In Supercomputing 2001, page http://www.sc2001.org. IEEE/ACM, 2001.Google Scholar
  98. 98.
    www.amath.washington.edu/∼rjl/amrclaw/.Google Scholar
  99. 99.
    www.astro.phys.ethz.ch/staff/walder/private/codes/A-MAZE/AMRCART/AMRCART.html.Google Scholar
  100. 100.
    www.amath.unc.edu/Faculty/mitran/bearclaw.html.Google Scholar
  101. 101.
    seesar.lbl.gov/ANAG/chombo/index.html.Google Scholar
  102. 102.
    cosmos.ucsd.edu/enzo.Google Scholar
  103. 103.
    flash.uchicago.edu.Google Scholar
  104. 104.
    astronomy.swin.edu.au/staff/aknebe/MLAPM/.Google Scholar
  105. 105.
    www.aip.de/groups/MHD/projects/NIRVANA/nirvana. html.Google Scholar
  106. 106.
    ct.gsfc.nasa.gov/paramesh/Users manual/amr.html.Google Scholar
  107. 107.
    www.llnl.gov/CASC/SAMRAI/.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michael L. Norman
    • 1
  1. 1.Laboratory for Computational Astrophysics at the Center for Astrophysics and Space SciencesUniversity of California at San DiegoLa JollaUSA

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