In wave scattering, standard frequency-domain solvers prescribe a plane‑wave “incident field” at an obstacle surface and enforce approximate outgoing conditions towards infinity (e.g., PMLs or local ABCs). However, a plane wave is neither incoming nor outgoing and therefore is not admissible smooth datum at infinity. In addition, this procedure is inconsistent in variable media: a constant‑index plane wave does not solve the background operator.
In this talk, I formulate wave scattering as a boundary‑value problem at null infinity. Using conformal compactification along null directions, past and future null infinity become numerically accessible boundaries on which the mathematically natural datum is a smooth incoming radiation profile with finite energy. Within Melrose’s geometric scattering framework, the solution induces radiation fields at null infinity, and the scattering map carries incoming to outgoing data.
I present this viewpoint for Helmholtz equations with unbounded, variable media. Radiation conditions are enforced at null infinity, eliminating artificial truncation, while directly computing the scattering amplitudes (and hence far‑field patterns) for obstacles and media. This method bridges Penrose’s global geometric picture with Melrose’s microlocal analysis.