  The Immersed Interface Method is employed to solve the time-varying electric
field equations around a three-dimensional vesicle. To achieve second-order
accuracy the implicit jump conditions for the electric potential, up to the
second normal derivative, are derived. The trans-membrane potential is
determined implicitly as part of the algorithm. The method is compared to an
analytic solution based on spherical harmonics and verifies the second-order
accuracy of the underlying discretization even in the presence of solution
discontinuities. A sample result for an elliptic interface is also presented.
