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.

References

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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

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Articles