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2009-02-10
A Generalized GPS Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix
By
Progress In Electromagnetics Research, Vol. 90, 121-136, 2009
Abstract
A generalized GPS (GGPS) algorithm is proposed for the problem of reducing the bandwidth and profile of the stiffness matrix in finite element problems. The algorithm has two key-points. Firstly and most importantly, more pseudo-peripheral nodes are found, used as the origins for generating more level structures, rather than only two level structures in the GPS (Gibbs-Poole-Stockmeyer) algorithm. A new level structure is constructed with all the level structures rooted at the pseudo-peripheral nodes, leading to a smaller level width than the level width of any level structure's in general. Secondly, renumbering by degree is changed to be sum of the adjacent nodes codes to make a better renumbering in each level. Simulation results show that the GGPS algorithm can reduce the bandwidth by about 37.63% and 8.91% and the profiles by 0.17% and 2.29% in average for solid models and plane models, respectively, compared with the outcomes of GPS algorithm. The execution time is close to the GPS algorithm. Empirical results show that the GGPS is superior to the GPS in reducing bandwidth and profile.
Citation
Qing Wang Yu-Chun Guo Xiao-Wei Shi , "A Generalized GPS Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix," Progress In Electromagnetics Research, Vol. 90, 121-136, 2009.
doi:10.2528/PIER09010512
http://www.jpier.org/PIER/pier.php?paper=09010512
References

1. Wang, Q., Q., Y. C. Guo, and X. W. Shi, "An improved matrix bandwidth and profile reduction algorithm in FEM problems," Progress In Electromagnetics Research Symposium, Hangzhou, China, 2008.

2. Amjadi, S. M. and M. Soleimani, "Design of band-pass waveguide filter using frequency selective surfaces loaded with surface mount capacitors based on split-field update FDTD method," Progress In Electromagnetics Research B, Vol. 3, 271-281, 2008.
doi:10.2528/PIERB07122402

3. Zhou, X. and G. W. Pan, "Application of physical spline finite element method (PSFEM) to fullwave analysis of waveguides ," Progress In Electromagnetics Research, PIER 60, 19-41, 2006.

4. Wei, X. C., E. P. Li, and Y. J. Zhang, "Application of the improved finite element-fast multipole method on large scattering problems," Progress In Electromagnetics Research, PIER 47, 49-60, 2004.

5. Doncker, P. D., "The use of tansfinite elements in the methods of moments applied to electromagnetic scattering by dielectric cylinders," Progress In Electromagnetics Research, PIER 25, 77-94, 2000.

6. Bedrosian, G., "High-performance computing for finite element methods in low-frequency electromagnetics," Progress In Electromagnetics Research, PIER 07, 57-110, 1993.

7. Vaish, A. and H. Parthasarathy, "Analysis of a rectangular waveguide using finite element method," Progress In Electromagnetics Research C, Vol. 2, 117-125, 2008.
doi:10.2528/PIERC08031801

8. Hernandez, L. M. A. and M. G. Quintillan, "A finite element method code to analyse waveguide dispersion," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 397-408, 2007.
doi:10.1163/156939307779367396

9. Jin, J. M., The Finite Element Method in Electromagnetics, Wiley, New York, 2002.

10. Cuthill, E. and J. Mckee, "Reducing the bandwidth of sparse symmetric matrices," Proceedings of the 1969 24th National Conference, 157-172, 1969.
doi:10.1145/800195.805928

11. Reid, J. K. and J. A. Scott, "Implementing Hager's exchange methods for matrix profile reduction," ACM Transcations on Mathematical Software, Vol. 28, No. 4, 377-391, 2002.
doi:10.1145/592843.592844

12. Chan, W. M. and A. George, "A lineartime implementation of the reverse Cuthill-McKee algorithm," BIT Numerical Mathematics, Vol. 20, No. 1, 8-14, 1980.
doi:10.1007/BF01933580

13. Gibbs, N. E., "Algorithm 509: A hybrid profile reduction algorithm [F1]," ACM Transactions on Mathematical Software, Vol. 2, No. 4, 378-387, 1976.
doi:10.1145/355705.355713

14. Gibbs, N. E., W. G. Poole, Jr., and P. K. Stockmeyer, "An algorithm for reducing the bandwidth and profile of a sparse matrix," SIAM Journal on Numerical Analysis, Vol. 13, No. 2, 236-250, 1976.
doi:10.1137/0713023

15. George, A. and J. W. H. Liu, "An implementation of a pseudoperipheral node finder," ACM Transactions on Mathematical Software, Vol. 5, No. 3, 284-295, 1979.
doi:10.1145/355841.355845

16. Souza, L. T. and D. W. Murray, "An alternative pseudoperipheral node finder for resequencing schemes," International Journal for Numerical Methods in Engineering, Vol. 36, No. 19, 3351-3379, 1993.
doi:10.1002/nme.1620361910

17. Tai, C. C. and Y. L. Pan, "Finite element method simulationof photoinductive imaging for cracks," Progress In Electromagnetics Research Letters, Vol. 2, 53-61, 2008.
doi:10.2528/PIERL07122807

18. Boutora, Y., N. Takorabet, R. Ibtiouen, and S. Mezani, "A new method for minimizing the bandwidth and profile of square matrices for triangular finite elements mesh," IEEE Transactions on Magnetics, Vol. 43, No. 4, 1513-1516, 2007.
doi:10.1109/TMAG.2007.891460