Fast algorithms for computing electrostatic geometric sensitivities

In this paper we show that for the standard piecewise-constant collocation schemes used in programs like FASTCAP, computing the change in electrostatic forces due to geometric perturbations is equivalent to resolving for the charge distribution given a potential generated by linearly varying dipole distributions. Second, we derive closed form analytic expressions for the potential due to the linearly varying dipole distributions. Third, results are given from implementing the dipole approach in the precorrected-FFT code FFTCAP and combining it with the adjoint method so as to rapidly compute the sensitivity of capacitances to parameter variations.