Efficient Jacobian Matrix Determination for H2 Representations of Nonlinear Electrostatic Surface Integral Equations

Authors

  • John C. Young Depatrment of Electrical & Computer Engineering University of Kentucky Lexington, KY USA
  • Robert J. Adams Depatrment of Electrical & Computer Engineering University of Kentucky Lexington, KY USA
  • Stephen D. Gedney Department of Electrical Engineering University of Colorado-Denver Denver, CO USA

Keywords:

corrosion-related fields, hierarchical matrices, nonlinear integral equation, randomized linear algebra

Abstract

In this paper, a nonlinear electrostatic surface integral equation is presented that is suitable for predicting corrosion-related fields. Nonlinear behavior arises due to electrochemical reactions at polarized surfaces. Hierarchical H2 matrices are used to compress the discretized integral equation for the fast solution of large problems. A technique based on randomized linear algebra is discussed for the efficient computation of the Jacobian matrix required at each iteration of a nonlinear solution.

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References

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.

W. Hackbusch, Hierarchical Matrices Algorithms and Analysis, Heidelberg: Springer, 2015, p. 1 online resource. [Online]. Available: http://dx.doi.org/10.1007/978-3-662-47324-5 MIT Access Only.

N. Halko, P. G. Martinsson, and J. A. Tropp, "Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions," vol. 53, no. 2, pp. 217-288, 2011.

R. A. Pfeiffer, J. C. Young, R. J. Adams, and S. D. Gedney, "Higher-order simulation of impressed current cathodic protection systems," Journal of Computational Physics, vol. 394, pp. 522-531, 2019/10/01/ 2019.

M. Bebendorf and S. Kunis, "Recompression techniques for adaptive cross aapproximation," The Journal of Integral Equations and Applications, vol. 21, no. 3, pp. 331-357, 2009.

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Published

2020-11-07

How to Cite

[1]
John C. Young, Robert J. Adams, and Stephen D. Gedney, “Efficient Jacobian Matrix Determination for H2 Representations of Nonlinear Electrostatic Surface Integral Equations”, ACES Journal, vol. 35, no. 11, pp. 1264–1265, Nov. 2020.

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