Constraining of the zero total surface charge in galvanic modelling

The galvanic problem is frequently solved by a Fredholm integral equation of the second kind based on a single layer source formulation. At higher conductivity contrasts between the model and its surroundings the homogeneous part of the integral equation approaches an eigenvalue equation. With infinite contrast the solution of this limiting integral equation is non‐unique, but in the subspace of zero total charge the solution is unique. This mathematical property of the integral equation is reflected in its numerical solution with the result that large numerical errors may appear and convergence of the solution becomes very slow. Errors are, for the most part, related to the computed excess charge generated in the numerical solution. The effect is studied by comparing the results computed from the solution of the integral equation alone with those computed from a particular solution where the requirement of zero total charge is used as a constraint. The model examples clearly show that the use of the constraint condition significantly improves the accuracy of the results.