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A parallel wavelet-based algebraic multigrid black-box solver and preconditioner. (English) Zbl 1244.65256
Summary: This work introduces a new parallel wavelet-based algorithm for algebraic multigrid method (PWAMG) using a variation of the standard parallel implementation of discrete wavelet transforms. This new approach eliminates the grid coarsening process in traditional algebraic multigrid setup phase simplifying its implementation on distributed memory machines. The PWAMG method is used as a parallel black-box solver and as a preconditioner in some linear equations systems resulting from circuit simulations and 3D finite elements electromagnetic problems. The numerical results evaluate the efficiency of the new approach as a standalone solver and as preconditioner for the biconjugate gradient stabilized iterative method.
MSC:
65T60Wavelets (numerical methods)
65Y05Parallel computation (numerical methods)
65F08Preconditioners for iterative methods
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Full Text: DOI
References:
[1] G. Haase, M. Kuhn, and S. Reitzinger, “Parallel algebraic multigrid methods on distributed memory computers,” SIAM Journal on Scientific Computing, vol. 24, no. 2, pp. 410-427, 2002. · Zbl 1014.65131 · doi:10.1137/S1064827501386237
[2] V. E. Henson and U. M. Yang, “BoomerAMG: a parallel algebraic multigrid solver and preconditioner,” Applied Numerical Mathematics, vol. 41, no. 1, pp. 155-177, 2002. · Zbl 0995.65128 · doi:10.1016/S0168-9274(01)00115-5
[3] H. de Sterck, U. M. Yang, and J. J. Heys, “Reducing complexity in parallel algebraic multigrid preconditioners,” SIAM Journal on Matrix Analysis and Applications, vol. 27, no. 4, pp. 1019-1039, 2006. · Zbl 1102.65034 · doi:10.1137/040615729
[4] M. Griebel, B. Metsch, D. Oeltz, and M. A. Schweitzer, “Coarse grid classification: a parallel coarsening scheme for algebraic multigrid methods,” Numerical Linear Algebra with Applications, vol. 13, no. 2-3, pp. 193-214, 2006. · Zbl 1174.65544 · doi:10.1002/nla.482
[5] A. J. Cleary, R. D. Falgout, V. E. Henson, and J. E. Jones, Coarse-Grid Selection for Parallel Algebraic Multigrid, Lawrence Livermore National Laboratory, Livermore, Calif, USA, 2000. · Zbl 0991.65133
[6] L. Yu. Kolotilina and A. Yu. Yeremin, “Factorized sparse approximate inverse preconditionings. I. Theory,” SIAM Journal on Matrix Analysis and Applications, vol. 14, no. 1, pp. 45-58, 1993. · Zbl 0767.65037 · doi:10.1137/0614004
[7] M. J. Grote and T. Huckle, “Parallel preconditioning with sparse approximate inverses,” SIAM Journal on Scientific Computing, vol. 18, no. 3, pp. 838-853, 1997. · Zbl 0872.65031 · doi:10.1137/S1064827594276552
[8] D. Hysom and A. Pothen, “A scalable parallel algorithm for incomplete factor preconditioning,” SIAM Journal on Scientific Computing, vol. 22, no. 6, pp. 2194-2215, 2000. · Zbl 0986.65048 · doi:10.1137/S1064827500376193
[9] P. Raghavan, K. Teranishi, and E. G. Ng, “A latency tolerant hybrid sparse solver using incomplete Cholesky factorization,” Numerical Linear Algebra with Applications, vol. 10, no. 5-6, pp. 541-560, 2003. · Zbl 1071.65065 · doi:10.1002/nla.327
[10] P. Raghavan and K. Teranishi, “Parallel hybrid preconditioning: incomplete factorization with selective sparse approximate inversion,” SIAM Journal on Scientific Computing, vol. 32, no. 3, pp. 1323-1345, 2010. · Zbl 1213.65052 · doi:10.1137/080739987
[11] C. Janna, M. Ferronato, and G. Gambolati, “A block Fsai-Ilu parallel preconditioner for symmetric positive definite linear systems,” SIAM Journal on Scientific Computing, vol. 32, no. 5, pp. 2468-2484, 2010. · Zbl 1220.65037 · doi:10.1137/090779760
[12] C. Janna and M. Ferronato, “Adaptive pattern research for block FSAI preconditioning,” SIAM Journal on Scientific Computing, vol. 33, no. 6, pp. 3357-3380, 2011. · Zbl 1273.65045
[13] M. Benzi and M. Tuma, “A comparative study of sparse approximate inverse preconditioners,” Applied Numerical Mathematics, vol. 30, no. 2-3, pp. 305-340, 1999. · Zbl 0949.65043 · doi:10.1016/S0168-9274(98)00118-4
[14] F. H. Pereira, S. L. L. Verardi, and S. I. Nabeta, “A wavelet-based algebraic multigrid preconditioner for sparse linear systems,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1098-1107, 2006. · Zbl 1107.65040 · doi:10.1016/j.amc.2006.04.057
[15] F. H. Pereira, M. F. Palin, S. L. L. Verardi, V. C. Silva, J. R. Cardoso, and S. I. Nabeta, “A wavelet-based algebraic multigrid preconditioning for iterative solvers in finite-element analysis,” IEEE Transactions on Magnetics, vol. 43, no. 4, pp. 1553-1556, 2007. · doi:10.1109/TMAG.2007.892468
[16] F. H. Pereira, M. M. Afonso, J. A. De Vasconcelos, and S. I. Nabeta, “An efficient two-level preconditioner based on lifting for FEM-BEM equations,” Journal of Microwaves and Optoelectronics, vol. 9, no. 2, pp. 78-88, 2010.
[17] T. K. Sarkar, M. Salazar-Palma, and C. W. Michael, Wavelet Applications in Engineering Electromagnetics, Artech House, Boston, Mass, USA, 2002.
[18] V. M. Garcıa, L. Acevedo, and A. M. Vidal, “Variants of algebraic wavelet-based multigrid methods: application to shifted linear systems,” Applied Mathematics and Computation, vol. 202, no. 1, pp. 287-299, 2008. · Zbl 1147.65027 · doi:10.1016/j.amc.2008.02.015
[19] A. Avudainayagam and C. Vani, “Wavelet based multigrid methods for linear and nonlinear elliptic partial differential equations,” Applied Mathematics and Computation, vol. 148, no. 2, pp. 307-320, 2004. · Zbl 1044.65092 · doi:10.1016/S0096-3003(02)00845-7
[20] D. de Leon, “Wavelet techniques applied to multigrid methods,” CAM Report 00-42, Department of Mathematics UCLA, Los Angeles, Calif, USA, 2000.
[21] G. Wang, R. W. Dutton, and J. Hou, “A fast wavelet multigrid algorithm for solution of electromagnetic integral equations,” Microwave and Optical Technology Letters, vol. 24, no. 2, pp. 86-91, 2000.
[22] R. S. Chen, D. G. Fang, K. F. Tsang, and E. K. N. Yung, “Analysis of millimeter wave scattering by an electrically large metallic grating using wavelet-based algebratic multigrid preconditioned CG method,” International Journal of Infrared and Millimeter Waves, vol. 21, no. 9, pp. 1541-1560, 2000. · Zbl 1170.78354
[23] F. H. Pereira and S. I. Nabeta, “Wavelet-based algebraic multigrid method using the lifting technique,” Journal of Microwaves and Optoelectronics, vol. 9, no. 1, pp. 1-9, 2010.
[24] J. M. Ford, K. Chen, and N. J. Ford, “Parallel implementation of fast wavelet transforms,” Numerical Analysis 39, Manchester University, Manchester, UK, 2001. · Zbl 0985.65037
[25] H. J. Sips and H. X. Lin, High Performance Computing Course MPI Tutorial, Delft University of Technology Information Technology and Systems, Delft, The Netherlands, 2002.
[26] F. Alessandri, M. Chiodetti, A. Giugliarelli et al., “The electric-field integral-equation method for the analysis and design of a class of rectangular cavity filters loaded by dielectric and metallic cylindrical pucks,” IEEE Transactions on Microwave Theory and Techniques, vol. 52, no. 8, pp. 1790-1797, 2004. · doi:10.1109/TMTT.2004.831583
[27] T. A. Davis, “Algorithm 849: a concise sparse Cholesky factorization package,” ACM Transactions on Mathematical Software, vol. 31, no. 4, pp. 587-591, 2005. · Zbl 1136.65311 · doi:10.1145/1114268.1114277
[28] D. A. Wood and M. D. Hill, “Cost-effective parallel computing,” Computer, vol. 28, no. 2, pp. 69-72, 1995. · doi:10.1109/2.348002