Time-dependent hyperbolic partial differential equations can be efficiently solved using adaptive mesh refinement, with a hierarchy of finer grid patches in regions where the solution is discontinuous or rapidly varying. These patches can be adjusted every few time steps to follow propagating waves. For many problems the primary interest is in tracking waves that reach one target location, perhaps after multiple reflections. The solution to an adjoint equation solved backward in time from the target location can be used to identify the regions that require refinement. These adjoint methods are incorporated in the Clawpack software for general hyperbolic problems and have been used in the GeoClaw software to track tsunami waves in the ocean that will reach a particular community of interest.

Randall LeVeque received his Ph.D. in Computer Science from Stanford in 1982 and has been at the University of Washington since 1985, where he is now Professor Emeritus of Applied Mathematics. He is a lead developer of the Clawpack and GeoClaw software packages, and the author of several books on numerical methods for differential equations. Current research interests are focused on algorithm and software development, particularly for tsunamis and other geophysical flows, and on development of probabilistic hazard assessment techniques. He is a Fellow of SIAM and the American Mathematical Society.