Vol. 39
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2012-02-12
Solving for Micro- and Macro-Scale Electrostatic Configurations Using the Robin Hood Algorithm
By
Progress In Electromagnetics Research B, Vol. 39, 1-37, 2012
Abstract
We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems. We illustrate the capabilities of this solver by studying two distinct geometry scales: (a) the electrostatic potential of a large volume beta-detector and (b) the field enhancement present at surface of electrode nano-structures. Geometries with elements numbering in the O(105) are easily modeled and solved without loss of accuracy. The technique has recently been expanded so as to include dielectrics and magnetic materials.
Citation
Joseph A. Formaggio, Predrag Lazic, Thomas Joseph Corona, Hrvoje Stefancic, Hrvoje Abraham, and Ferenc Gluck, "Solving for Micro- and Macro-Scale Electrostatic Configurations Using the Robin Hood Algorithm," Progress In Electromagnetics Research B, Vol. 39, 1-37, 2012.
doi:10.2528/PIERB11112106
References

1. Chen, A. H.-D. and D. T. Cheng, "Heritage and early history of the boundary element method," Engineering Analysis with Boundary Elements, Vol. 29, 268, 2005.
doi:10.1016/j.enganabound.2004.12.001

2. Hall, W. S., The Boundary Element Method, Kluwer Academic Publishers, The Netherlands, 1994.
doi:10.1007/978-94-011-0784-6

3. Cartwright, D. J., Underlying Principles of the Boundary Element Method, WIT Press, Boston, 2001.

4. Lothar, G., M. Kogl, and M. Wagner, Boundary Element Methods for Engineers and Scientists, 1st edition, Springer-Verlag, Berlin Heidelberg, 2003.

5. Brebbia, C. A. and R. Butterfield, Boundary Element Techniques in Engineering, 1st edition, Butterworth Publishers Inc., 1980.

6. Brebbia, C. A. and S. Walker, "Formal equivalence of direct and indirect boundary element methods," Appl. Math. Modelling, Vol. 2, 132-134, Jun. 1978.
doi:10.1016/0307-904X(78)90052-5

7. Lazic, P., H. Stefancic, and H. Abraham, "The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer," J. Comput. Phys., Vol. 213, 117, 2006.
doi:10.1016/j.jcp.2005.08.006

8. Lazic, P., H. Stefancic, and H. Abraham, "The robin hood method a new view on differential equations," Engineering Analysis with Boundary Elements, Vol. 32, 76, 2008.
doi:10.1016/j.enganabound.2007.06.004

9. Szilagyi, M., Electron and Ion Optics, Plenum Press, New York, 1988.
doi:10.1007/978-1-4613-0923-9

10. Poljak, D. and C. A. Brebbia, "Boundary Element Methods for Electrical Engineers," 1st edition, WIT Press, Boston, 2005.

11. Jackson, J. D., "Classical Electrodynamics," 2nd edition, John Wiley and Sons, New York, 1975.

12. Rao, S., T. Sarkar, and R. F. Harrington, "The electrostatic field of conducting bodies in multiple dielectric media," IEEE Transactions on Microwave Theory and Techniques, Vol. 32, 1441, 1974.

13. Garcia de Abajo, F. J. and A. Howie, "Retarded field calculation of electron energy loss in inhomogeneous dielectrics," Phys. Rev. B, Vol. 65, 115418, 2002.
doi:10.1103/PhysRevB.65.115418

14. , , , http://www.artcalc.com/.

15. Anita, H. M., Numerical Methods for Scientists and Engineers, Birkhauser verlag, Basel, Boston, Berlin, 2002.

16. Strang, G., Computational Science and Engineering, Wellesley-Cambridge Press, Wellesley, MA, 2007.

17. Khronos Open CL Working Group, The OpenCL Specification, , version 1.0.29, http://www.khronos.org/registry/cl/specs/opencl-1.0.29.pdf., 2008.

18. Geuzaine, C. and J.-F. Remacle, "Gmsh: A finite element mesh generator with built-in pre- and post-processing facilities,", http://www.geuz.org/gmsh/, 1996.

19. Angrik, J., et al. "The KATRIN Design Report,", FZK Scientific Report 7090, www-ik.fzk.de/tritium/publications/documents/De signReport2004 , 12Jan2005.pdf, 2005.

20. Weinheimer, C., et al. "High precision measurement of the tritium β spectrum near its endpoint and upper limit on the neutrino mass," Phys. Lett., Vol. B460, 219, 1999.
doi:10.1088/0022-3735/13/1/018

21. Lobashev, V. M., et al. "Direct search for mass of neutrino and anomaly in the tritium beta-spectrum," Phys. Lett., Vol. B460, 227, 1999.
doi:10.1039/b711486a

22. Beamson, G., et al. "The collimating and magnifying properties of a superconducting field photoelectron spectrometer," Journal of Physics E, Vol. 13, 64, 1980.
doi:10.1116/1.3531929

23. Myroshnychenko, V., J. Rodriguez-Fernandez, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzan, and F. J. Garcia de Abajo, "Modelling the optical response of gold nanoparticles," Chem. Soc. Rev., Vol. 37, 1792, 2008.
doi:10.1103/PhysRevB.65.115418

24. Persaud, A., I. Allen, M. R. Dickinson, and T. Schenkel, "Development of a compact neutron source based on field ionization processes," J. Vac. Sci. Technol. B, Vol. 29, 02B107, 2011.
doi:10.1116/1.588345

25. Garcia de Abajo, F. J. and A. Howie, "Retarded field calculation of electron energy loss in inhomogeneous dielectrics," Phys. Rev. B, Vol. 65, 115418, 2002.
doi:10.1038/nmat2944

26. Jensen, K. L., "Improved Fowler-Nordheim equation for field emission from semiconductors," J. Vac. Sci. Technol. B, Vol. 13, 516, 1995.
doi:10.1038/nnano.2008.174

27. Banan Sadeghian, R. and M. Saif Islam, "Ultralow-voltage field-ionization discharge on whiskered silicon nanowires for gas-sensing applications," Nat. Mater., Vol. 10, 135, 2011.
doi: --- Either ISSN/ISBN or Series/Volume title must be supplied.

28. Keefer, E. W., B. R. Botterman, M. I. Romero, A. F. Rossi, and G. W. Gross, "Carbon nanotube coating improves neuronal recordings," Nat. Nano, Vol. 3, 434, 2008.
doi: --- Either ISSN/ISBN or Series/Volume title must be supplied.

29. Bonard, J.-M., N. Weiss, H. Kind, T. Stockli, L. Forro, K. Kern, and A. Chatelain, "Tuning the field emission properties of patterned carbon nanotube films," Adv. Mater., Vol. 13, 184, 2001.

30. Wang, Z. and N. Koratkar, "Suppressing electrostatic screening in nanostructured electrode arrays," J. Nanosci. Nanotechno., Vol. 6, 1979, 2006.
doi:10.1098/rspa.1928.0091

31. Lin, M. C.-C., H. J. Lai, M. S. Lai, M. H. Yang, and A. K. Li, "Characteristic of field emission from carbon nanotubes synthesized from different sources," Mater. Phys. Mech., Vol. 4, 138, 2001.
doi:10.1146/annurev.anchem.1.031207.112814

32. Fowler, H. and L. Nordheim, "Electron emission in intense electric fields," Proc. R. Soc. A, Vol. 119, 173, 1928.
doi:10.1021/jp106245a

33. Stiles, P. L., J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, "Surface-enhanced raman spectroscopy," Annu. Rev. Anal. Chem., Vol. 1, 601, 2008.
doi:10.1038/nature07378

34. Jin, M., V. Pully, C. Otto, A. van den Berg, and E. T. Carlen, "High-density periodic arrays of self-aligned subwavelength nanopyramids for surface-enhanced raman spectroscopy," J. Phys. Chem. C, Vol. 114, 21953, 2010.
doi:10.1209/0295-5075/91/46003

35. Camara, C. G., J. V. Escobar, J. R. Hird, and S. J. Putterman, "Correlation between nanosecond X-ray flashes and stickslip friction in peeling tape," Nature, Vol. 455, 1089, 2008.

36. Lazic, P. and B. N. J. Persson, "Surface-roughnessinduced electric-field enhancement and triboluminescence," Europhys. Lett., Vol. 91, 46003, 2010.

37. Sivula, K., F. Le Formal, and M. Gratzel, "Solar water splitting: Progress using hematite (α-Fe2O3) photoelectrodes," Chem. Sus. Chem., Vol. 4, 432, 2011.

38. Birtles, A. B., B. J. Mayo, and A. W. Bennett, "Defocussing of charged particle beams transmitted through meshes," PROC. IEE, Vol. 120, No. 2, 213-220, Feb. 1973.

39. Hudson, R. G. and J. Lipka, A Table of Integrals, Stanhope Press, Boston, 1917.

40. Bowman, F. and F. A. Gerard, Higher Calculus, Cambridge University Press, 1967.