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


  • 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


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


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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