This talk will present a method for accurately computing the solution of a 
wave equation by decomposing it onto a largely incomplete set of 
eigenfunctions of the Helmholtz operator, chosen at random. The recovery 
method is the ell-1 minimization of compressed sensing. The guarantees of 
success are based on three estimates for the wave equation, namely 1) an 
L^1 estimate, 2) a result of extension  of the eigenfunctions, and 3) an 
eigenvalue gap estimate. These estimates hold in the one-dimensional case 
when the medium has small bounded variation. In practice, this 
``compressive" strategy is a natural way of parallelizing wave simulations 
for memory-intensive applications.  Joint work with Gabriel Peyre.