Adaptive mesh refinement for characteristic grids

General Relativity and Gravitation

Volumn 43, Issue 5, 2011, Pages 1211-1251

  Thornburg, Jonathan ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Adaptive mesh refinement; Berger Oliger algorithm; Characteristic coordinates; Characteristic grids; Finite differencing

Indexed keywords

EID: 79955078971     PISSN: 00017701     EISSN: 15729532     Source Type: Journal    
DOI: 10.1007/s10714-010-1096-z     Document Type: Article

References (84)

1. Anderson M., Hirschmann E. W., Liebling S. L., Neilsen D.: Class. Quant. Grav. 23(22), 6503 (2006).
2. Barack L.: Class. Quant. Grav. 26(21), 213001 (2009).
3. Barack L., Ori A.: Phys. Rev. D 66(8), 084022 (2002).
4. Berger, M. J.: Adaptive mesh refinement for hyperbolic partial differential equations. PhD thesis, Stanford University, University Microfilms #DA 83-01196 (1982).
5. Berger M. J.: SIAM J. Sci. Stat. Comput. 7(3), 904 (1986).
6. Berger M. J., Colella P.: J. Comput. Phys. 82(1), 64 (1989).
7. Berger M. J., Oliger J.: J. Comput. Phys. 53(3), 484 (1984).
8. Brown, D. L., Chesshire, G. S., Henshaw, W. D., Quinlan, D. J.: In: Heath, M. T., Torczon, V., Astfalk G. (eds.) Eighth SIAM Conference on Parallel Processing for Scientific Computing, Minneapolis, 14-17 Mar 1997. ISBN 978-0898713954 (1999).
9. Brown, D. L., Henshaw, W. D., Quinlan, D. J.: Object oriented methods for interoperable scientific and engineering. In: Henderson, M. E., Lyons, S. L. (eds.) Proceedings of the SIAM Interdisciplinary Workshop on Object Oriented Methods for Interoperable Scientific and Engineering Computing, Yorktown Heights, 21-23 Oct 1998, pp. 245-255. ISBN 978-0898714456 (1999).
10. Brügmann B.: Phys. Rev. D 54(12), 7361 (1996).
11. Brügmann B., González J. A., Hannam M., Husa S., Sperhake U., Tichy W.: Phys. Rev. D 77(2), 024027 (2008).
12. Brügmann B., Tichy W., Jansen N.: Phys. Rev. Lett. 92(21), 211101 (2004).
13. Buchman L. T., Sarbach O. C. A.: Class. Quant. Grav. 23(23), 6709 (2006).
14. Buchman L. T., Sarbach O. C. A.: Class. Quant. Grav. 24(12), S307 (2007).
15. Burgarelli D., Kischinhevsky M., Biezuner R. J.: J. Comp. Appl. Math. 196(1), 115 (2006).
16. Burko L. M., Ori A.: Phys. Rev. D 56(12), 7820 (1997).
17. Char B., Geddes K. O., Gentleman W. M., Gonnet G. H.: The design of maple: a compact, portable, and powerful computer algebra system. In: Hulzen, J. A. (ed.) Lecture Notes in Computer Science, vol. 162, pp. 101-115. Springer, Berlin (1983).
18. Choptuik, M. W.: A study of numerical techniques for radiative problems in general relativity. PhD thesis, University of British Columbia, Vancouver (1986).
19. Choptuik M. W.: In: Evans, C., Finn, L., Hobill, D. (eds) Frontiers in Numerical Relativity, pp. 206-221. Cambridge University Press, Cambridge (1989).
20. Choptuik M. W.: Phys. Rev. D 44(10), 3124 (1991).
21. Choptuik M. W.: In: d'Inverno, R. (ed.) Approaches to Numerical Relativity, pp. 202-222. Cambridge University Press, Cambridge (1992).
22. Choptuik M. W.: Phys. Rev. Lett. 70(1), 9 (1993).
23. Choptuik, M. W.: ad: An implementation of the Berger-Oliger mesh refinement algorithm for the wave equation in spherical symmetry. http://laplace. phas. ubc. ca/Members/matt/Doc/ad. ps (1994).
24. Choptuik M. W., Hirschmann E. W., Liebling S. L., Pretorius F.: Class. Quant. Grav. 20(9), 1857 (2003).
25. Choptuik M. W., Hirschmann E. W., Liebling S. L., Pretorius F.: Phys. Rev. D 68(4), 044007 (2003).
26. Colella, P., Graves, D. T., Keen, N. D., Ligocki, T. J., Martin, D. F., McCorquodale, P. W., Modiano, D., Schwartz, P. O., Sternberg, T. D., Straalen, B. V.: Chombo Software Package for AMR Applications. https://seesar. lbl. gov/anag/chombo/index. html (2009).
27. Colella, P., Graves, D. T., Keen, N. D., Ligocki, T. J., Martin, D. F., McCorquodale, P. W., Modiano, D., Schwartz, P. O., Sternberg, T. D., Straalen, B. V.: Chombo Software Package for AMR Applications: Design Document. Technical Report, Applied Numerical Algorithms Group, Computational Research Division, Lawrence Berkeley National Laboratory. https://seesar. lbl. gov/anag/chombo/ChomboDesign-3. 0. pdf (2009).
28. Deiterding, R.: AMROC: Blockstructured Adaptive Mesh Refinement in Object-Oriented C++. http://amroc. sourceforge. net/index. htm (2005).
29. Deiterding, R.: Construction and application of an AMR algorithm for distributed memory computers. In: Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, 3-5 Sep 2003. Lecture Notes in Computational Science and Engineering, vol. 41, Part II, pp. 361-372. Springer, Berlin (2005).
30. Deiterding R.: Construction and application of an AMR algorithm for distributed memory computers. Int. J. Comp. Sci. Eng. 1(1/2/3), 64 (2006).
31. Dursi, L. J., Zingale, M.: Efficiency gains from time refinement on AMR meshes and explicit timestepping. In: Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, 3-5 Sep 2003. Lecture Notes in Computational Science and Engineering, vol. 41, part II, pp. 103-113. Springer, Berlin (2005).
32. Givoli D.: J. Comp. Phys. 94(1), 1 (1991).
33. Gómez R., Winicour J.: J. Math. Phys. 33(4), 1445 (1992).
34. Gómez R., Winicour J., Isaacson R.: J. Comp. Phys. 98(1), 11 (1992).
35. Goodale, T., Allen, G., Lanfermann, G., Massó, J., Radke, T., Seidel, E., Shalf, J.: In: Vector and Parallel Processing-VECPAR 2002, 5th International Conference. Lecture Notes in Computer Science. Springer, Berlin (2003).
36. Goodale, T., Massó, J., Allen, G., Lanfermann, G., Shalf, J.: The Cactus Code. http://www. cactuscode. org (1999).
37. Gundlach C., Price R., Pullin J.: Phys. Rev. D 49(2), 883 (1994).
38. Haas R.: Phys. Rev. D 75(12), 124011 (2007).
39. Hamadé R. S., Stewart J. M.: Class. Quant. Grav. 13(3), 497 (1996).
40. Henshaw, W. D., Brown, D. L., Chesshire, G. S., Quinlan, D. J.: The Overture Code. http://acts. nersc. gov/overture/ (2002).
41. Hornung, R. D., Kohn, S. R.: The use of object-oriented design patterns in the SAMRAI structured AMR framework. In: Henderson, M. E., Lyons, S. L. (eds.) Proceedings of the SIAM Interdisciplinary Workshop on Object Oriented Methods for Interoperable Scientific and Engineering Computing, Yorktown Heights, 21-23 Oct 1998, pp. 235-244. ISBN 978-0898714456 (1999).
42. Hornung R. D., Kohn S. R.: Concurr. Comput. Pract. Exp. 14(5), 347 (2002).
43. Hornung, R. D., Kohn, S. R.: SAMRAI: Structured Adaptive Mesh Refinement Application Infrastructure. https://computation. llnl. gov/casc/SAMRAI/index. html (2002).
44. Hornung R. D., Wissink A. M., Kohn S. R.: Eng. Comput. 22(3-4), 181 (2006).
45. Husa S., González J. A., Hannam M., Brügmann B., Sperhake U.: Class. Quant. Grav. 25(10), 105006 (2008).
46. Kidder L. E., Lindblom L., Scheel M. A., Buchman L. T., Pfeiffer H. P.: Phys. Rev. D 71(6), 064020 (2005).
47. Kreiss, H. O., Oliger, J.: Methods for the approximate solution of time dependent problems. GARP publication series No. 10, Geneva (1973).
48. Lea, D.: A Memory Allocator. http://gee. cs. oswego. edu/dl/html/malloc. html. Accessed 24 Aug 2009 (2000).
49. Lehner L., Liebling S. L., Reula O.: Class. Quant. Grav. 23(16), S421 (2006).
50. LeVeque R. J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge (2002) ISBN 0-521-00924-3.
51. LeVeque R. J.: Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM Press, Philadelphia (2007) ISBN 978-0-898716-29-0.
52. Liebling S. L.: Phys. Rev. D 66(4), 041703 (2002).
53. Liebling S. L.: Class. Quant. Grav. 21(16), 3995 (2004).
54. Lijewski, M., Beckner, V. E., Rendleman, C. A.: CCSE Software Infrastructure: BoxLib and AmrLib. http://seesar. lbl. gov/ccse/Software/index. html (2006).
55. Lousto C. O.: Class. Quant. Grav. 22(15), S543 (2005).
56. Lousto C. O., Price R. H.: Phys. Rev. D 56(10), 6439 (1997).
57. MacNeice P., Olson K. M., Mobarry C., de Fainchtein R., Packer C.: Comp. Phys. Comm. 126(3), 330 (2000).
58. Martel K., Poisson E.: Phys. Rev. D 66(8), 084001 (2002).
59. Mitra, S., Parashar, M., Browne, J.: DAGH: User's Guide. http://userweb. cs. utexas. edu/users/dagh/ (1995).
60. Olson K. M.: PARAMESH: a parallel adaptive grid tool. In: Deane, A., Ecer, A., Brenner, G., Emerson, D., McDonough, J., Periaux, J., Satofuka, N., Tromeur-Dervout, D. (eds) Proceedings of the Parallel CFD Conference, College Park, Elsevier, Amsterdam (2006).
61. Olson, K. M., MacNeice, P.: Paramesh: Parallel Adaptive Mesh Refinement. http://www. physics. drexel. edu/~olson/paramesh-doc/Users_manual/amr. html (1999).
62. Olson, K. M., MacNeice, P.: An overview of the PARAMESH AMR package and some of its applications. In: Plewa, T., Linde, T., Weirs, G. V. (eds.) Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, 3-5 Sep 2003. Lecture Notes in Computational Science and Engineering, vol. 41. Springer, Berlin (2005).
63. Parashar, M., Browne, J. C.: System engineering for high performance computing software: the HDDA/DAGH infrastructure for implementation of parallel structured adaptive mesh refinement. In: IMA Volume on Structured Adaptive Mesh Refinement (SAMR) Grid Methods, pp. 1-18. Springer, Berlin (2000).
64. Parashar, M., Li, X.: In: Parashar, M., Li, X., Chandra, S. (eds.) Advanced Computational Infrastructures for Parallel and Distributed Applications, pp. 249-263. Wiley, New York. ISBN 978-0-470-07294-3 (2009).
65. Pretorius, F.: AMRD Reference Manual. http://laplace. phas. ubc. ca/Doc/pamr/AMRD_ref. pdf (2002).
66. Pretorius, F.: Numerical simulations of gravitational collapse. PhD thesis, University of British Columbia, Vancouver (2002).
67. Pretorius, F.: PAMR Reference Manual. http://laplace. phas. ubc. ca/Doc/pamr/PAMR_ref. pdf (2002).
68. Pretorius F., Choptuik M.: J. Comput. Phys. 218(1), 246 (2006).
69. Pretorius F., Lehner L.: J. Comput. Phys. 198(1), 10 (2004).
70. Rendleman C. A., Beckner V. E., Lijewski M., Crutchfield W., Bell J. B.: Comput. Vis. Sci. 3, 147 (2000).
71. Richtmyer R. D., Morton K.: Difference Methods for Initial Value Problems, 2nd edn. Kreiger, Malabar, FL (1994) ISBN 0-89464-763-6.
72. Rinne O.: Class. Quant. Grav. 23(22), 6275 (2006).
73. Rinne O., Buchman L. T., Scheel M. A., Pfeiffer H. P.: Class. Quant. Grav. 26(7), 075009 (2009).
74. Rinne O., Lindblom L., Scheel M. A.: Class. Quant. Grav. 24(16), 4053 (2007).
75. Ruiz M., Rinne O., Sarbach O.: Class. Quant. Grav. 24(24), 6349 (2007).
76. Schnetter, E.: CARPET: A Mesh Refinement Driver for CACTUS. http://www. carpetcode. org (2001).
77. Schnetter E., Hawley S. H., Hawke I.: Class. Quant. Grav. 21(6), 1465 (2004).
78. Seiler J., Szilágyi B., Pollney D., Rezzolla L.: Class. Quant. Grav. 25(17), 175020 (2008).
79. Su, J. Z., Wen, T., Yelick, K. A.: Compiler and Runtime Support for Scaling Adaptive Mesh Refinement Computations in Titanium. Technical Report UCB/EECS-2006-87, Electrical Engineering and Computer Sciences Department, University of California at Berkeley. http://www. eecs. berkeley. edu/Pubs/TechRpts/2006/EECS-2006-87. pdf (2006).
80. Tornberg A.-K., Engquist B.: J. Comp. Phys. 200(2), 462 (2004).
81. Wald, R. M.: General Relativity. The University of Chicago Press, Chicago. ISBN 0-226-87032-4 (hardcover), 0-226-87033-2 (paperback) (1984).
82. Welling, J. S.: Numerical calculations in the characteristic initial value problem in general relativity. PhD thesis, University of Pittsburgh, Pittsburgh, university Microfilms Order #84-11, 762 (1983).
83. Wilson, P. R., Johnstone, M. S., Neely, M., Boles, D.: Dynamic storage allocation: a survey and critical review. In: Baker, H. G. (ed.) Proceedings of the 1995 International Workshop on Memory Management. Lecture Notes in Computer Science, vol. 986, pp. 1-116. Springer, Berlin. ISBN 978-3540603689 (1995).
84. Winicour, J.: Living Rev. Relat. 12(3) http://www. livingreviews. org/lrr-2009-3 (2009).