A shape variational approach for determining potential lines using the boundary element method

A shape optimization (i.e., variational) approach is adopted in this paper to determine potential lines. Solution of the primary potential problem is accomplished by the boundary element method (BEM). To find the position of any potential line a suitably defined objective functional is minimized using structural optimization techniques. In particular, the sensitivity analysis expression of the objective functional with respect to the shape variation of internal curves is derived by employing the material derivative concept. With the internal potential and potential derivative values available through the BEM solution of the potential problem, the correct shapes of the potential contours are found by a shape minimization procedure, After checking the numerical results by a one-dimensional problem, potential contours for two-dimensional example problems are determined and plotted.