
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
HwangCheng Wang, Kai Hwang, "Multicoloring of GridStructured PDE Solvers on SharedMemory Multiprocessors," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 11, pp. 11951205, November, 1995.  
BibTex  x  
@article{ 10.1109/71.476191, author = {HwangCheng Wang and Kai Hwang}, title = {Multicoloring of GridStructured PDE Solvers on SharedMemory Multiprocessors}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {6}, number = {11}, issn = {10459219}, year = {1995}, pages = {11951205}, 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 GridStructured PDE Solvers on SharedMemory Multiprocessors IS  11 SN  10459219 SP1195 EP1205 EPD  11951205 A1  HwangCheng 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,“mstep preconditioned conjugate gradient methods,” SIAM J. Sci. Stat. Comp., vol. 6, pp. 452463, 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. 746757, 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. 103134, 1986.
[5] T.F. Chan and Y. Saad,“Multigrid algorithms on the hypercube multiprocessor,” IEEE Trans. Computers, pp. 969977, 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. 309332, 1985, Also Report LBL14856, Lawrence Berkeley Laboratory, 1982.
[7] C.C. Douglas and W.L. Miranker,“Constructive interference in parallel algorithms,” SIAM J. Numer. Anal., vol. 25, pp. 376398, 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 selfadjoint difference equations,” SIAM J. Numer. Anal., vol. 5, pp. 559573, 1968.
[10] H.C. Elman and E. Agron,“Ordering techniques for the preconditioning of conjugate gradient methods on parallel computers,” Technical Report UMIACSTR8853, 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. 87100, 1990.
[12] K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programmability. McGrawHill, 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. 105120, 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. 9196.
[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. 175, 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 Mmatrix,” Math. Comp, vol. 31, pp. 148162, 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. 117138, 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. 778795, 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. 149240, 1985.
[20] E.L. Poole and J.M. Ortega,“Multicolor ICCG methods for vector computers,” SIAM J. Numer. Anal., vol. 24, pp. 1,3941,418, 1987.
[21] Y. Saad,“Krylov subspace methods on supercomputers,” SIAM J. Sci. Stat. Comp., vol. 10, no. 6, pp. 1,2001,232, 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 sharedmemory multiprocessors,” PhD thesis, Department of Electrical EngineeringSystems, Univ. of Southern California, 1992.
[24] H.C. Wang and K. Hwang,“Multicoloring for fast sparse matrixvector multiplication in solving PDE problems,” Proc. Int’l Conf. Parallel Processing,St. Charles, Ill., Aug. 1993, vol. 3: Algorithms and Applications, pp. 215222.
[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., McGrawHill, New York, 1989.