Much of the computational cost involved in full-waveform inversion comes from the solution of the wave equation in a large domain. These computations must be done for the entire domain through which we expect waves to pass for a particular survey, despite the fact that our region of interest is often significantly smaller. In addition to the wasted time spent propagating waves through less important parts of the model, computing updates on the entire domain may result in slower convergence of the inversion algorithm due to the larger model space. This can be especially important in 4D seismic monitoring, where we often see the majority of changes within a small subregion of the total domain, such as the reservoir. We present a local wave solver that accurately computes the solution of the wave equation within only a subdomain of the region covered by the survey, representing a significant cost saving in the computation of full-waveform inversion. We also show how this solver can improve the resulting velocity estimates in full-waveform inversion for time-lapse applications and observe that the local solver requires fewer iterations to converge than does the full-domain solver.