Locally Corrected Nystrom Discretization for Impressed Current Cathodic Protection Systems

Authors

  • John C. Young Department of Electrical and Computer Engineering University of Kentucky, Lexington, KY 40506, USA
  • Robert A. Pfeiffer Department of Electrical and Computer Engineering University of Kentucky, Lexington, KY 40506, USA
  • Robert J. Adams Department of Electrical and Computer Engineering University of Kentucky, Lexington, KY 40506, USA
  • Stephen D. Gedney Department of Electrical and Computer Engineering University of Colorado-Denver, Denver, CO 80204, USA

Keywords:

Impressed current cathodic protection systems, integral equations, locally corrected Nyström method

Abstract

A high-order locally corrected Nystrom discretization for analyzing impressed current cathodic protection systems is presented. Non-linear polarization curves are incorporated using a Newton-Raphson scheme. A Schur complement scheme is introduced to handle large domains with small electrodes. The methods are characterized in terms of error convergence and computation time by comparing to the analytic solution for a sphere and hemisphere.

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References

J. M. Chuang, N. G. Zamani, and C. C. Hsuing, “Some computational aspects of BEM simulation of cathodic protection systems,” Applied Mathematical Modelling, vol. 11, pp. 371-379, October 1987.

N. G. Zamani, J. M. Chuang, and J. F. Porter, “BEM simulation of cathodic protection systems employed in infinite electrolytes,” International Journal for Numerical Methods in Engineering, vol. 45, pp. 605-620, 1987.

J. F. Yan, S. N. R. Pakalapati, T. V. Nguyen, R. E. White, and R. B. Griffin, “Mathematical modeling of cathodic protection using the boundary element method with a nonlinear polarization curve,” Journal of The Electrochemical Society, vol. 139, pp. 1932-1936, July 1, 1992.

W. Sun, G. Yuan, and Y. Ren, “Iterative algorithms for impressed cathodic protection systems,” International Journal for Numerical Methods in Engineering, vol. 49, pp. 751-768, 2000.

R. Pfieffer, “High-order Integral Equation Methods for Quasi-Magnetostatic and Corrosion-Related Field Analysis with Maritime Applications,” Ph.D., Electrical & Computer Engineering, University of Kentucky, Lexington, KY, 2018.

J. C. Young, R. Pfeiffer, R. J. Adams, and S. D. Gedney, “Locally corrected Nyström discretization for impressed current cathodic protection systems,” presented at the 2018 International Applied Computational Electromagnetics Society Symposium (ACES), Denver, CO, 2018.

S. D. Gedney, “On deriving a locally corrected Nyström scheme from a quadrature sampled moment method,” IEEE Transactions on Antennas and Propagation, vol. 51, pp. 2402-2412, September 2003.

S. D. Gedney and J. C. Young, “The locally corrected Nystrom method for electromagnetics,” in Computational Electromagnetics: Recent Advances and Engineering Applications, R. Mittra, Ed., New York: Springer, pp. 149-198, 2014.

L. F. Canino, J. J. Ottusch, M. A. Stalzer, J. L. Visher, and S. M. Wandzura, “Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nyström discretization,” Journal of Computational Physics, vol. 146, pp. 627-663, 1998.

G. C. Hsiao and W. L. Wendland, Boundary Integral Equations. vol. 164, Berlin: SpringerVerlag, 2008.

R. Pfeiffer, J. C. Young, and R. J. Adams, “Numerical characterization of divergence-conforming constrained basis functions for surface integral equations,” IEEE Transactions on Antennas and Propagation, vol. 65, pp. 1867-1874, 2017.

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Published

2021-07-22

How to Cite

[1]
John C. Young, Robert A. Pfeiffer, Robert J. Adams, and Stephen D. Gedney, “Locally Corrected Nystrom Discretization for Impressed Current Cathodic Protection Systems”, ACES Journal, vol. 33, no. 10, pp. 1081–1086, Jul. 2021.

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