Title: Explicit local time-stepping methods for wave propagation
Abstract
Adaptivity and mesh refinement are certainly key for the efficient numerical simulation of wave phenomena in complex geometry. Locally refined meshes, however, severely constrain the time-step of any explicit time-marching scheme due to the CFL stability condition governed by the smallest elements in the mesh. When mesh refinement is restricted to a small subregion, the use of implicit methods, or a tiny time-step in the entire computational domain, are a high price to pay. Explicit local time-stepping (LTS) methods overcome that bottleneck due to a few small elements by using smaller time-steps precisely where the smallest elements in the mesh are located. When combined with a finite element discretization in space with an essentially diagonal mass matrix, the resulting time-marching schemes remain fully explicit and thus inherently parallel.
