Preprints
Introduction
I have produced a few papers so far in my career. I have not concentrated on one specific area. Instead I have worked in a number of theoretical areas and several application that are related. The topics include multigrid, numerical simulation of flames, domain decomposition, numerical linear algebra, iterative methods, or esoteric computing methods.
The papers are in chronological order. You may download them in either of two Adobe formats: PostScript or PDF (PDF). The files are gzipped in either case. The PDF files can be read on any computer using the Adobe Acrobat Reader, version 5.0 or later (I use version 5, however). I use gv -antialias %s as my application helper when using netscape under Linux for both PostScript and PDF file viewing.
An odd problem with version 5.0 of Acrobat Reader has been reported for Windows NT 4.0 and Windows 2000. This may exist for other versions of Windows. You download a large PDF file and can only render the first page. The cure seems to be to go back and click on the hyperlink again. If the file is preloaded, the problem does not seem to exist. The full version 5.0 Acrobat package that costs money (versus just the free Reader) might not have this problem.
1. C. C. Douglas, G. Haase, U. Langer, A Tutorial on Elliptic PDE Solvers and their Parallelization, vol. 16, Software, Environments, and Tools (SET) series, SIAM Books, Philadelphia, 2003.
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http://ec-securehost.com/SIAM/SE16.html Online Resources
Tutorial
1. C. C. Douglas, J. J. Hu, M. Kowarschik, and U. Rüde, Very High Performance Cache Based Techniques for Iterative Methods, December, 2003 edition.
Publications1. C. C. Douglas, Multi-grid algorithms for solving elliptic partial differential equations, Ph.D. Thesis, Yale University, New Haven, CT, 1982.
2. C. C. Douglas, Abstract multi-grid with applications to elliptic boundary-value problems, in Elliptic Problem Solvers II, G. Birkhoff and A. Schoenstadt, editors, Academic Press, New York, 1984, pp. 453-466.
3. C. C. Douglas, Multi-grid algorithms with applications to elliptic boundary-value problems, SIAM Journal on Numerical Analysis, 21 (1984), pp. 236-254.
4. C. C. Douglas, A multigrid optimal order solver for elliptic boundary value problems: the finite difference case, in Advances in Computer Methods for Partial Differential Equations - V. R. Vichnevetsky and R.S. Stepleman, editors, IMACS, New Brunswick, NJ, 1984, pp. 369-373.
5. R. E. Bank, and C. C. Douglas, Sharp estimates for multigrid rates of convergence with general smoothing and acceleration, SIAM Journal on Numerical Analysis, 22 (1985), pp. 617-633.
6. C. C. Douglas, A multilevel solver for boundary value problems, appeared in a special joint issue on numerical simulation of VLSI devices of IEEE Transactions on Electrons, 32 (1985), pp. 1987-1991 and IEEE Transactions on Computer Aided Design, 4 (1985), pp. 431-435.
7. R. E. Bank, and C. C. Douglas, An efficient implementation of the SSOR and ILU preconditionings, Applied Numerical Mathematics, 1 (1985), pp. 489-492.
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8. C. C. Douglas, Parallel multigrid techniques, in Proceedings of a Conference on Domain Decomposition and Fast Iterative Techniques, J. Bramble and L. Wahlbin, editors, Mathematical Sciences Institute, Cornell University, Ithaca, NY, 1986.
9. C. C. Douglas, S. C. Ma and W. L. Miranker, Generating parallel algorithms through multigrid and aggregation-disaggregation techniques, in Computational Acoustics: Algorithms and Applications, D. Lee, M. H. Schultz, and R. L. Sternberg, editors, Elsevier Science Publishers (North Holland), 1988, pp. 133-147.
10. C. C. Douglas W. L. Miranker, Constructive interference in parallel algorithms, SIAM Journal on Numerical Analysis, 25 (1988), pp. 376-398.
11. C. C. Douglas, Michael Henderson, Susumu Horiguchi, Willard L. Miranker, Barry F. Smith, and Andrew Winkler, The interaction of numerics and machines, Informationstechnik-IT, 30 (1988), pp. 83-98.
12. C. C. Douglas and W. L. Miranker, Some nontelescoping parallel algorithms based on serial multigrid-aggregation-disaggregation techniques, in Multigrid Methods, S. F. McCormick, editor, Marcel Dekker, New York, 1988, pp. 167-176.
13. C. C. Douglas, Parallel multigrid and domain reduction methods, in Proceedings of the IBM Symposium on Parallel Processing, Poughkeepsie, NY, 1988, pp. 43-48.
14. C. C. Douglas, The parallel domain reduction method in three dimensions, in preliminary version of the Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods, Volume 2, S. F. McCormick and J. Mandel, editors, Computational Mathematics Group, University of Colorado at Denver, Denver, CO, 1989.
15. F. Brezzi, C. C. Douglas, and L. D. Marini, A parallel domain reduction method, in Numerical Methods for Partial Differential Equations, 5 (1989), pp. 195-202.
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16. C. C. Douglas and B. F. Smith, Using symmetries and antisymmetries to analyze a parallel multigrid algorithm, SIAM Journal on Numerical Analysis, 26 (1989), pp. 1439-1461.
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17. C. C. Douglas and J. Mandel, The domain reduction method: high way reduction in three dimensions and convergence with inexact solvers, in Fourth Copper Mountain Conference on Multigrid Methods, J. Mandel, S. F. McCormick, J. E. Dendy, C. Farhat, G. Lonsdale, S. V. Parter, J. W. Ruge, and K. Stüben, editors, SIAM Books, Philadelphia, 1989, pp. 149-160.
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18. C. C. Douglas, A note on a statistical model of computation for parallel, distributed, or serial computers, in Proceedings of the Copper Mountain Conference on Iterative Methods, T. Manteuffel, editor, Computational Mathematics Group, University of Colorado at Denver, Denver, CO, 1990.
19. C. C. Douglas, A variation of the Schwarz alternating method: the domain decomposition reduction method, in Domain Decomposition Methods for Partial Differential Equations III, T. Chan, R. Glowinski, J. Périaux, and O. B. Widlund, editors, SIAM Books, Philadelphia, 1990, pp. 191-201.
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20. C. C. Douglas and W. L. Miranker, The multilevel principal applied to sorting, BIT, 30 (1990), pp. 178-195.
21. C. C. Douglas, J. Mandel, and W. L. Miranker, Fast hybrid solution of algebraic systems, SIAM Journal on Scientific and Statistical Computing, 11 (1990), pp. 1073-1086.
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22. C. C. Douglas, Parallel multigrid, domain decomposition, and projection methods are all similar, Transactions of the American Nuclear Society, 62 (1990), pp. 270-271.
23. C. C. Douglas and W. L. Miranker, Beyond massive parallelism: numerical computation using associative tables, Parallel Computing, 16 (1990), pp. 1-25.
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24. C. C. Douglas and J. Douglas, Jr., Towards a general convergence theory under few assumptions for abstract multilevel algorithms, in Proceedings of the Fifth Copper Mountain Conference on Multigrid Methods, Volume 1, S. F. McCormick and J. Mandel, editors, Computational Mathematics Group, University of Colorado at Denver, Denver, CO, 1991.
25. C. C. Douglas, Practical uses of domain reduction methods, in Domain Decomposition Methods for Partial Differential Equations IV, R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux, and O. B. Widlund, editors, SIAM Books, Philadelphia, 1991, pp. 27-34.
26. C. C. Douglas, An almost assumptionless convergence theory for the full approximation scheme or multiple coarse space multigrid algorithms, in Multigrid Methods: Special Topics and Applications II, W. Hackbusch and U. Trottenberg, editors, GMD-Studien 189, GMD St. Augustin, Germany, 1991, pp. 69-79.
27. C. C. Douglas, A tupleware approach to domain decomposition methods, Applied Numerical Mathematics, 8 (1991), pp. 353-373.
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28. C. C. Douglas, The effect of interpolation on the rate of convergence in two level algorithms for elliptic partial differential equations, in Proceedings of the Second Copper Mountain Conference on Iterative Methods, Volume 1, T. Manteuffel, editor, Computational Mathematics Group, University of Colorado at Denver, Denver, CO, 1992.
29. C. C. Douglas and J. Mandel, A group theoretic approach to the domain reduction method, Computing, 48 (1992), pp. 73-96.
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30. C. C. Douglas, Parallel multilevel and multigrid methods, in Applications on Advanced Architecture Computers column, SIAM News, 25 (1992), pp. 14-15.
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31. C. C. Douglas and J. Douglas, Jr., A greatly simplified theory for parallel multigrid or projection methods, in Proceedings of the Fifth SIAM Conference on Parallel Processing for Scientific Computing, J. Dongarra, K. Kennedy, P. Messina, D. Sorensen, and R. Voigt (editors), SIAM Books, Philadelphia, 1992, pp. 105-110.
32. C. C. Douglas, MGNet: a multigrid and domain decomposition network, 1992. ACM SIGNUM Newsletter, 27 (1992), pp. 2-8.
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33. C. C. Douglas and J. Douglas, Jr., A unified convergence theory for abstract multigrid or multilevel algorithms, serial and parallel, SIAM Journal on Numerical Analysis, 30 (1993), pp. 136-158.
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34. R. E. Bank and C. C. Douglas, Sparse matrix multiplication package (SMMP), Advances in Computational Mathematics, 1 (1993), pp. 127-137.
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35. C. C. Douglas, Implementing abstract multigrid or multilevel methods, in Sixth Copper Mountain Conference on Multigrid Methods, N. D. Melson (ed.), NASA, Langley, VA, 1993, pp. 127-141.
36. C. C. Douglas and A. Ern, Numerical solution of flame sheet problems with and without multigrid methods, in Sixth Copper Mountain Conference on Multigrid Methods, N. D. Melson (ed.), NASA, Langley, VA, 1993, pp. 143-157.
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37. C. C. Douglas, M. Heroux, G. Slishman, and R. M. Smith, GEMMW: A portable Level~3 BLAS Winograd variant of Strassen's matrix-matrix multiply algorithm, Journal of Computational Physics, 110 (1994), pp. 1-10.
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Research Report: PostScript PDF
38. C. C. Douglas, Some remarks on completely vectorizing point Gauss-Seidel while using the natural ordering, Advances in Computational Mathematics, 2 (1994), pp. 215-222.
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39. C. C. Douglas, D. A. George, and M. E. Henderson, Object classes for numerical analysis, OONSKI'94: Proceedings of the second annual object-oriented numerics conference, Rogue Wave Software, Corvallis, OR, 1994, pp. 32-49.
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40. C. C. Douglas, A generalized multigrid theory in the style of standard iterative methods, Multigrid Methods IV, P. W. Hemker and P. Wesseling (eds.), Birkäuser, Basil, 1994, pp. 19-34.
41. C. C. Douglas and G. Slishman, Variants of matrix-matrix multiplication for Fortran-90, ACM SIGNUM Newsletter, 29 (1994), pp. 4-6.
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42. C. C. Douglas, A. Ern, and M. D. Smooke, Numerical simulation of laminar diffusion flames, SIAM News, 27/9 (1994), pp. 1, 12-13, 17. In revised form in Applications on Advanced Architecture Computers, G. Astfalk (ed.), SIAM Books, Philadelphia, 1996, pp. 243-254.
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43. C. C. Douglas, J. Douglas, Jr. and D. E. Fyfe, A multigrid unified theory for non-nested grids and/or quadrature, East-West Journal of Numerical Mathematics, 2 (1994), pp. 285-294.
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44. C. C. Douglas, Madpack: A family of abstract multigrid or multilevel solvers, Computational and Applied Mathematics, 14 (1995), pp. 3-20.
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45. A. Deshpande, S. Malhotra, C. C. Douglas, and M. H. Schultz, A rigorous analysis of time domain parallelism. Parallel Algorithms and Applications, 6 (1995), pp. 53-62.
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46. B. Moon, G. Patnaik, R. Bennett, D. Fyfe, A. Sussman, J. Saltz, and K. C. C. Douglas, Runtime support and dynamic load balancing strategies for structured adaptive applications, in Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, D. H. Bailey, P. E. Bjørstad, J. R. Gilbert, M. D. Mascagni, R. Schrieber, H. D. Simon, V. J. Torczon, L. T. Watson (eds.), SIAM Books, Philadelphia, 1995, pp. 575-580.
47. C. C. Douglas, T. G. Mattson, and M. H. Schultz, Experimental results for data sharing on high performance multiprocessors, in Toward Teraflop Computing and New Grand Challenge Applications, R. K. Kalia and P. Vashishta (eds.) Nova Science Publications, Commack, NY, 1995, 13 pages.
48. A. Ern, C. C. Douglas, and M. D. Smooke, Detailed chemistry modeling of laminar diffusion flames on parallel computers, International Journal of Supercomputer Applications and High Performance Computing, 9 (1995), pp. 167-186.
49. C. C. Douglas, Caching in with multigrid algorithms: problems in two dimensions Parallel Algorithms and Applications, 9 (1996), pp. 195-204.
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50. C. C. Douglas, A. Ern, and M. D. Smooke. High performance computing and numerical simulation of flames ZAMM, 76 (1996), pp. 49-52.
51. C. C. Douglas, A sparse matrix approach to abstract multilevel solvers on serial and parallel computers. ZAMM, 76 (1996), pp. 139-142.
52. J. Philbin, J. Edler, O. J. Anshus, C. C. Douglas, and K. Li, Thread scheduling for cache locality, in Proceedings of the Seventh ACM Conference on Architectural Support for Programming Languages and Operating Systems, Cambridge, Massachusetts, October 1996, pp. 60-73.
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53. C. C. Douglas, A review of numerous parallel multigrid methods, in Applications on Advanced Architecture Computers, G. Astfalk (ed.), SIAM Books, Philadelphia, 1996, pp. 187-202.
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54. C. C. Douglas, J. Douglas, Jr. and D. E. Fyfe, A note on multigrid theory for non-nested grids and/or quadrature, in Seventh Copper Mountain Conference on Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas (eds.), NASA, Langley, VA, 1996, pp. 255-264.
55. C. C. Douglas, Multigrid methods in science and engineering, IEEE Comput. Sci. Eng., 3 (1997), pp. 55-68.
56. C. C. Douglas, A. Ern, and M. D. Smooke, Multigrid solution of flame sheet problems on serial and parallel computers, Parallel Algorithms and Applications, 10 (1997), pp. 225-236.
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57. C. C. Douglas, S. Malhotra, and M. H. Schultz, A characterization of mapping unstructured grids onto structured grids and using multigrid as a preconditioner, BIT, 37 (1997), pp. 661-677.
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58. C. C. Douglas, A. Ern, and M. D. Smooke, Numerical simulation of flames using multigrid methods, in Iterative Methods in Scientific Computation, J. Wang, M. B. Allen, B. M. Chen, and T. Mathew (eds.), IMACS Series in Computational and Applied Mathematics, Vol. 4, New Brunswick, 1998, pp. 149-154.
59. C. C. Douglas, S. Malhotra, and M. H. Schultz, ``Transpose free'' alternating direction smoothers for serial and parallel multigrid methods, in Advances in Computational Mathematics, Z. Chen, Y. Li, C. Micchelli, and Y. Xu (eds.), Marcel-Dekker, New York, 1998, pp. 39-52.
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60. C. C. Douglas, S. Malhotra, and M. H. Schultz, Parameter choices for ADI-like methods on parallel computers, Comput. Appl. Math., 17 (1999), pp. 217-231.
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61. C. C. Douglas, S. Malhotra, and M. H. Schultz, Parallel multigrid with ADI-like smoothers in two dimensions, in Fifth European Multigrid Conference Special Topics and Applications, W. Hackbusch and G. Wittum (eds.), 1998, pp. 47-57.
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62. C. C. Douglas, U. Rüde, J. Hu, and M. L. Bittencourt, Cache based multigrid on unstructured grids, in Virtual Proceedings of the Tenth GAMM Workshop on Parallel Multigrid Methods, M. Griebel (ed.), MGNet Virtual Proceedings Series, Cos Cob, 1999.
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63. C. C. Douglas, J. Hu, W. Karl, M. Kowarschik, U. Rüde, C. Weiss, Cache optimization for structured and unstructured grid multigrid, Elect. Trans. Numer. Anal., 10 (2000), pp. 25-40.
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64. C. C. Douglas, G. Haase, J. Hu, W. Karl, M. Kowarschik, U. Rüde, C. Weiss, Portable memory hierarchy techniques for PDE solvers, Part I, SIAM News 33/5 (2000), pp. 1, 8-9.
65. C. C. Douglas, G. Haase, J. Hu, W. Karl, M. Kowarschik, U. Rüde, C. Weiss, Portable memory hierarchy techniques for PDE solvers, Part II, SIAM News 33/6 (2000), pp. 1, 10-11, 16.
66. C. C. Douglas, J. Hu, M. Iskandarani, M. Kowarschik, U. Rüde, C. Weiss, Maximizing cache memory usage for multigrid algorithms, in Multiphase Flows and Transport in Porous Media: State of the Art, Z. Chen, R. E. Ewing, and Z.-C. Shi (eds.), Lecture Notes in Physics, Vol. 552, Springer-Verlag, Berlin, 2000, pp. 234-247.
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67. C. C. Douglas and K. M. Walters, Variable order cascadic multigrid algorithms, Proceedings of ECCOMAS 2000, Barcelona, Spain, 2000, 10 pages.
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68. C. C. Douglas, J. Hu, W. Karl, M. Kowarschik, U. Rüde, C. Weiss, Fixed and adaptive cache aware algorithms for multigrid methods, in Multigrid Methods VI, E. Dick, K. Riemslagh, and J. Vierendeels (eds.), Lecture Notes in Computational Sciences, Springer-Verlag, Berlin, 2000, pp. 87-93.
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69. C. C. Douglas, J. Hu, M. Iskandarani, Preprocessing costs of cache based multigrid, in Proceedings of the Third European Conference on Numerical Mathematics and Advanced Applications, P. Neittaanmäki, T. Tiihonen, and P. Tarvainen (eds.), World Scientific, Singapore, 2000, pp. 362-370.
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70. C. C. Douglas, G. Haase, M. Iskandarani, High performance multi-layer ocean modeling, in Proceedings of the First MIT Conference on Computational Solid and Fluid Mechanics, K. J. Bathe (ed.), 2001, 5 pages.
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71. M. L. Bittencourt, C. C. Douglas, R. A. Feijóo, Non-nested multigrid methods for linear problems, Numer. Meth. PDE, 17 (2001), 313-331.
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72. C. C. Douglas, J. Hu, J. Ray, D. T. Thorne, and R. S. Tuminaro, Fast, adaptively refined computational elements in 3D, in Computational Science - ICCS 2002, P. M. A. Sllot, C. J. K. Tan, J. J. Dongarra, and A. G. Hoekstra (eds.), 3 (2002), pp. 774-783.
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73. M. L. Bittencourt, C. C. Douglas, R. A. Feijóo, Adaptive non-nested multigrid methods, Eng. Comput., 19 (2002), pp. 158-176.
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74. C. C. Douglas, G. Haase, and M. Iskandarani, An acceleration procedure for the spectral element ocean model formulation of the shallow water equations, Contemporary Mathematics, 295 (2002), pp. 153-158. Also in Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment, Z. Chen and R. E. Ewing (eds.).
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75. C. C. Douglas and D. T. Thorne, A note on cache memory methods for multigrid in three dimensions, Contemporary Mathematics, 306 (2002), pp. 167-177. Also in Recent Advances in Numerical Methods for Partial Differential Equations and Applications, X. Feng (ed.).
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76. C. C. Douglas, G. Haase, M. Iskandarani, An additive Schwarz preconditioner for the spectral element ocean model formulation of the shallow water equations, Elec. Trans. Numer. Anal., (15) 2003, pp. 18-28.
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77. C. C. Douglas, G. Haase, and S. Reitzinger, Special solution strategies inside a spectral ocean element model, Math. Models Meth. Applied Sci. (M3AS), 13 (2003), pp. 1-14.
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78. C. C. Douglas, Y. Efendiev, R. Ewing, R. Lazarov, M. R. Cole, C. R. Johnson, and G. Jones, Virtual telemetry middleware for DDDAS, in Computational Sciences - ICCS 2003, P. M. A. Sllot, D. Abramson, J. J. Dongarra, A. Y. Zomaya, and Yu. E. Gorbachev (eds.), 4 (2003), pp. 279-288.
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79. S. Kazaa and J. Zhang, and C. C. Douglas, Preconditioned multigrid simulation of an axisymmetric laminar diffusion flames, Mathematical and Computer Modeling, 38 (2003), pp. 269-279.
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80. C. C. Douglas, M. R. Cole, Y. Efendiev, R. Ewing, V. Ginting, G. Jones, C. R. Johnson, R. Lazarov, C. Shannon, and J. Simpson, A note on dynamic data driven application simulation (DDDAS) using virtual telemetry, ICPACE 2003, J. Zou and X. Chi (eds.), Chinese University of Hong Kong, 2003, pp. 193-198.
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81. C. C. Douglas and G. Haase, Algebraic multigrid and Schur complement strategies within a multilayer spectral element ocean model, Contemporary Math., 329 (2003), pp. 89-98. Also, in Current Trends in Scientific Computing: ICM 2002 Beijing Satellite Conference on Scientific Computing, Z. Chen, R. Glowinski, and K. Li (eds.).
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82. C. C. Douglas, J. Hu, J. Ray, D. T. Thorne, and R. Tuminaro, Cache aware multigrid for variable coefficient elliptic problems on adaptive mesh refinement hierarchies, Numerical Linear Algrebra and Applications, 11 (2004), pp. 173-187.
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83. C. C. Douglas, C. Shannon, Y. Efendiev, R. Ewing, V. Ginting, R. Lazarov, M. R. Cole, G. Jones, C. R. Johnson, and J. Simpson, Telemetry-Driven Application Simulations, in Computational Sciences - ICCS 2004, M. Bubak, G. D. van Albada, P. M. A. Sloot, and J. J. Dongarra (eds.), 3 (2004), pp. 701-708.
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84. J. Mandel, M. Chen, L. P. Franca, C. Johns, A. Puhalskii,, J. L. Coen, C. C. Douglas, R. Kremens, A. Vodacek, W. Zhao, A Note on Dynamic Data Driven Wildfire Modeling, in Computational Sciences - ICCS 2004, M. Bubak, G. D. van Albada, P. M. A. Sloot, and J. J. Dongarra (eds.), 3 (2004), pp. 725-731.
85. C. C. Douglas, D. T. Thorne, J. Hu, J. Ray, and R. S. Tuminaro, Cache aware multigrid on tadaptively refined structured meshes, Proceedings of ECCOMAS 2004, Jyväskylä, Finland, 24-28 July 2004, P. Neittaanmaki, T. Rossi, S. Korotov, E. Onate, J. Periaux, and D. Knoerzer (eds.), 18 pages.
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Papers in Progress
C. C. Douglas, C. Shannon, Y. Efendiev, R. Ewing, V. Ginting, R. Lazarov, M. R. Cole, G. Jones, C. R. Johnson, and J. Simpson, Using a virtual telemetry methodology for dynamic data driven application simulations, to appear in Dynamic Data Driven Applications Systems, F. Darema (ed.), Kluwer, Amsterdam, 2004.
- J. Mandel, M. Chen, J. L. Coen, C. C. Douglas, L. P. Franca, C. Johns, R. Kremens, A. Puhalskii, A. Vodacek, and W. Zhao, Using a virtual telemetry methodology for dynamic data driven application simulations, to appear in Dynamic Data Driven Applications Systems, F. Darema (ed.), Kluwer, Amsterdam, 2004.
- C. C. Douglas, G. Haase, and J. Hu, The state of quasi-unstructured grid cache aware multigrid, submitted June, 2002.
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- C. C. Douglas, G. Haase, U. Langer, Parallel ADI smoothers for multigrid, in preparation, 2004.
NSF Reports
- A. Deshmukh, C. C. Douglas, M. Ball, R. E. Ewing, C. R. Johnson, C. Kesselman, C. Lee, and W. Powell, Dynamic data-driven application systems: creating a dynamic and symbiotic coupling of application/simulations with measurements/experiments, 2000, 28 pages.
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Orphans
These papers stand on their own, but are orphaned. The first one was accepted for publication by a now defunct publisher. The next two were combined into a single paper, but are clearer in original form.
- C. C. Douglas, U. Rüde, J. Hu, and M. L. Bittencourt, A guide to designing cache aware multigrid algorithms, in Proceedings of Concepts of Numerical Software, W. Hackbusch and G. Wittum (eds.), 1998.
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- M. Bittencourt, C. C. Douglas, R. A. Feijóo, Non-nested and Non-structured Multigrid Methods Applied to Elastic Problems. Part I: The Two-Dimensional Case.
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- M. Bittencourt, C. C. Douglas, R. A. Feijóo, Non-nested and Non-structured Multigrid Methods Applied to Elastic Problems. Part II: The Three-Dimensional Case.
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