Vol. 96
Latest Volume
All Volumes
PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2021-02-13
Memory Reduced Half Hierarchal Matrix (h -Matrix) for Electrodynamic Electric Field Integral Equation
By
Progress In Electromagnetics Research Letters, Vol. 96, 91-96, 2021
Abstract
This letter shows 50 percent memory saving for a regular Hierarchal Matrix (H-matrix) by converting it to symmetric H-matrix for large electrodynamic problems. Only the upper diagonal near-field and compressed far-field matrix blocks of the H-matrix are stored. Far-field memory saving is achieved by computing and keeping the upper diagonal far-field blocks leading to compressed column block U and row block V at a level. Due to symmetry, the lower diagonal far-field H-matrix compressed column is the transpose of V, and the compressed row block is the transpose of U. Storage and computation of lower diagonal blocks are not required. Similarly, in the case of near-field, only the upper diagonal near-field blocks are computed and stored. Numerical results show that the proposed memory reduction procedure retains the accuracy and cost of regular H-matrix.
Citation
Yoginder Kumar Negi , "Memory Reduced Half Hierarchal Matrix (h -Matrix) for Electrodynamic Electric Field Integral Equation," Progress In Electromagnetics Research Letters, Vol. 96, 91-96, 2021.
doi:10.2528/PIERL20120805
http://www.jpier.org/PIERL/pier.php?paper=20120805
References

1. Harrington, R. F., Field Computation by Moment Methods, Wiley-IEEE Press, New York, 1993.
doi:10.1109/9780470544631

2. Gibson, W. C., The Method of Moments in Electromagnetics, CRC Press, 2014.
doi:10.1007/PL00005410

3. Chew, W. C., J. M. Jin, E. Michielssen, and J. Song, Fast Efficient Algorithms in Computational Electromagnetics, Artech House, Boston, London, 2001.
doi:10.1109/20.996112

4. Bebendorf, M., "Approximation of boundary element matrices," Numerische Mathematik, Vol. 86, No. 4, 565-589, Jun. 2000.
doi:10.1007/s006070050015

5. Kurz, S., O. Rain, and S. Rjasanow, "The adaptive cross-approximation technique for the 3-D boundary element method," IEEE Transactions on Magnetics, Vol. 38, No. 2, 421-424, Mar. 2002.
doi:10.1109/20.996112

6. Hackbusch, W., "A sparse matrix arithmetic based on H-matrices. Part I: Introduction to Hmatrices," Computing, Vol. 62, No. 2, 89-108, 1999.
doi:10.1007/s006070050015

7. Hackbusch, W. and B. N. Khoromskij, "A sparse H-matrix arithmetic. Part II: Application to multi-dimensional problems," Computing, Vol. 64, 21-47, 2000.
doi:10.1049/iet-map.2009.0229

8. Borm, S., L. Grasedyck, and W. Hackbusch, "Hierarchical matrices," Lecture Notes, 21, 2003.
doi:10.1109/TAP.1982.1142818

9. Chai, W. and D. Jiao, "H and H2 matrix-based fast integral-equation solvers for large-scale electromagnetic analysis," IET Microwaves, Antennas and Propagation, No. 10, 1583-1596, 2010.
doi:10.1109/TAP.1965.1138406

10. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 3, 409-418, May 1982.
doi:10.1109/TAP.2013.2292079

11. Andreasen, M., "Scattering from bodies of revolution," IEEE Transactions on Antennas and Propagation, Vol. 13, No. 2, 303-310, 1965.
doi:10.1016/j.laa.2013.03.001

12. Su, T., D. Ding, Z. Fan, and R. Chen, "Efficient analysis of EM scattering from bodies of revolution via the ACA," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 2, 983-985, 2013.
doi:10.1109/MCSE.1998.7102081

13. Benner, P. and T. Mach, "The LR Cholesky algorithm for symmetric hierarchical matrices," Linear Algebra and Its Applications, Vol. 439, No. 4, 1150-1166, 2013.
doi:10.1216/JIE-2009-21-3-331

14. Kapur, S. and D. E. Long, "IES3: Efficient electrostatic and electromagnetic solution," IEEE Computer Science and Engineering, Vol. 5, No. 4, 60-67, Oct.–Dec. 1998.
doi:10.1109/MCSE.1998.7102081

15. Bebendorf, M. and S. Kunis, "Recompression techniques for Adaptive Cross Approximation," Journal of Integral Equations and Applications, Vol. 21, No. 3, 331-357, 2009.
doi:10.1049/iet-map.2020.0292

16. Negi, Y. K., V. P. Padhy, and N. Balakrishnan, "Re-compressed H-matrices for fast electric field integral equation," IEEE-International Conference on Computational Electromagnetics (ICCEM 2020), Singapore, Aug. 24–26, 2020.

17. Negi, Y. K., N. Balakrishnan, and S. M. Rao, "Symmetric near-field Schur's complement preconditioner for hierarchal electric field integral equation solver," IET Microwaves, Antennas and Propagation, Vol. 14, No. 14, 1846-1856, Aug. 2020.
doi:10.1049/iet-map.2020.0292