ADAPTIVE MULTI-TIME-STEP METHODS FOR DYNAMIC CRACK PROPAGATION
Problems in structural dynamics that involve rapid evolution of the material at multiple scales of length and time are challenging to solve numerically. One such problem is that of a structure un- dergoing fracture, where the material in the vicinity of a crack front may experience high stresses and strains while the remainder of the structure may be unaffected by it. Usually, such problems are solved using numerical methods based on a finite element discretization in space and a finite difference time-stepping scheme to capture dynamic response. Regions of interest within the struc- ture, where high transients are expected, are usually modeled with a fine discretization in space and time for better accuracy. In other regions of the model where the response does not change rapidly, a coarser discretization suffices and helps keep the computational cost down. This variation in spatial and temporal discretization is achieved through domain decomposition and multi-time-step coupling methods which allow the use of different levels of mesh discretization and time-steps in different regions of the mesh.