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| Hwang-Cheng Wang, Kai Hwang, "Multicoloring of Grid-Structured PDE Solvers on Shared-Memory Multiprocessors," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 11, pp. 1195-1205, November, 1995. | |||
| BibTex | x | ||
| @article{ 10.1109/71.476191, author = {Hwang-Cheng Wang and Kai Hwang}, title = {Multicoloring of Grid-Structured PDE Solvers on Shared-Memory Multiprocessors}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {6}, number = {11}, issn = {1045-9219}, year = {1995}, pages = {1195-1205}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.476191}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Parallel and Distributed Systems TI - Multicoloring of Grid-Structured PDE Solvers on Shared-Memory Multiprocessors IS - 11 SN - 1045-9219 SP1195 EP1205 EPD - 1195-1205 A1 - Hwang-Cheng Wang, A1 - Kai Hwang, PY - 1995 KW - Parallel processing KW - conjugate gradient methods KW - multicoloring KW - sparse matrix KW - PDE solvers KW - memory access conflicts KW - cache saturation KW - multiprocessor performance. VL - 6 JA - IEEE Transactions on Parallel and Distributed Systems ER - | |||
[1] L. Adams,“m-step preconditioned conjugate gradient methods,” SIAM J. Sci. Stat. Comp., vol. 6, pp. 452-463, 1985.
[2] Alliant Computer Systems Corp., FX/Series Product Summary, 1987.
[3] A.J. Bernstein,“Analysis of programs for parallel processing,” IEEE Trans. Elec. Computers, pp. 746-757, Oct. 1966.
[4] J.H. Bramble,J.E. Pasciak,, and A.H. Schatz,“The construction of preconditioners for elliptic problems by substructuring: I,” Math. Comp., vol. 47, no. 175, pp. 103-134, 1986.
[5] T.F. Chan and Y. Saad,“Multigrid algorithms on the hypercube multiprocessor,” IEEE Trans. Computers, pp. 969-977, Nov. 1986.
[6] P. Concus,G.H. Golub,, and G. Meurant,“Block preconditioning for the conjugate gradient method,” SIAM J. Sci. Stat. Comp., vol. 6, pp. 309-332, 1985, Also Report LBL-14856, Lawrence Berkeley Laboratory, 1982.
[7] C.C. Douglas and W.L. Miranker,“Constructive interference in parallel algorithms,” SIAM J. Numer. Anal., vol. 25, pp. 376-398, 1988.
[8] I.S. Duff, R. Grimes, and J. Lewis, “Sparse Matrix Test Problems,” ACM Trans. Mathematical Software, vol. 15, pp. 1–14, Mar. 1989.
[9] T. Dupont,R.P. Kendall,, and H.H. Rachford, Jr.,“An approximate factorization procedure for solving self-adjoint difference equations,” SIAM J. Numer. Anal., vol. 5, pp. 559-573, 1968.
[10] H.C. Elman and E. Agron,“Ordering techniques for the preconditioning of conjugate gradient methods on parallel computers,” Technical Report UMIACS-TR-88-53, UMIACS, Univ. of Maryland, 1988.
[11] I. Garcia,J.J. Merelo,J.D. Bruguera,, and E.L. Zapata,“Parallel quadrant interlocking factorization on hypercube computers,” Parallel Computing, vol. 15, pp. 87-100, 1990.
[12] K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programmability. McGraw-Hill, 1993.
[13] K. Hwang and H.C. Wang,“A multigrid Schwarz alternating method for parallel solution of elliptic PDE problems,” Proc. Int’l Conf. on Advances in Parallel Computing, D.J. Evans et al., Ed., pp. 105-120, 1989.
[14] R.B. Lee,“Empirical results on the speedup, efficiency, redundancy, and quality of parallel computations,” Proc. Int’l Conf. on Parallel Processing, Aug. 1980, pp. 91-96.
[15] O.A. McBryan,P.O. Frederickson,J. Linden,A. Schuller,K. Solchenbach,K. Stuben,C.A. Thole,, and U. Trottenberg,“Multigrid methods on parallel computers: A survey of recent developments,” Impact Comput. Sci. Eng., vol. 3, pp. 1-75, 1991.
[16] J.A. Meijerink and H.A. van der Vorst,“An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix,” Math. Comp, vol. 31, pp. 148-162, 1977.
[17] R. Melhem and K. Ramarao,“Multicolor reordering of sparse matrices resulting from irregular grids,” ACM Trans. Math. Software, vol. 14, no. 2, pp. 117-138, 1988.
[18] N.M. Nachtigal,S.C. Reddy,, and L.N. Trefethen,“How fast are nonsymmetric matrix iterations?” SIAM J. Matrix Anal. Appl., vol. 13, no. 3, pp. 778-795, 1992.
[19] J.M. Ortega and R.G. Voigt,“Solution of partial differential equations on vector and parallel computers,” SIAM Rev., vol. 27, no. 2, pp. 149-240, 1985.
[20] E.L. Poole and J.M. Ortega,“Multicolor ICCG methods for vector computers,” SIAM J. Numer. Anal., vol. 24, pp. 1,394-1,418, 1987.
[21] Y. Saad,“Krylov subspace methods on supercomputers,” SIAM J. Sci. Stat. Comp., vol. 10, no. 6, pp. 1,200-1,232, 1989.
[22] R. Schreiber and W. Tang,“Vectorizing the conjugate gradient method,” Proc. Symp. CYBER 205 Applications,Ft. Collins, Colo., 1982.
[23] H.C. Wang,“Parallelization of iterative PDE solvers on shared-memory multiprocessors,” PhD thesis, Department of Electrical Engineering-Systems, Univ. of Southern California, 1992.
[24] H.C. Wang and K. Hwang,“Multicoloring for fast sparse matrix-vector multiplication in solving PDE problems,” Proc. Int’l Conf. Parallel Processing,St. Charles, Ill., Aug. 1993, vol. 3: Algorithms and Applications, pp. 215-222.
[25] M.J. Wolfe,“Automatic vectorization, data dependence, and optimizations for parallel computers,” Parallel Processing for Supercomputing and Artificial Intelligence, K. Hwang and DeGroot, Eds., chap. 11., McGraw-Hill, New York, 1989.

