Obstacle Scattering as Seen by R.K. and R.K.

We recount some of Ralph Kleinman’s scientific achievements in obstacle scattering for time-harmonic waves by reporting on two topics where R.K. and R.K. interacted mathematically. The first topic is the problem of nonuniqueness for the classical boundary integral equations for the direct scattering problem and the second is the development of numerical methods for the inverse scattering problem.