In this section we describe spatial and temporal discretization and solution techniques for the governing elastodynamics equations, which are performed in parallel. We also describe the sequential phase, which consists of a mesh generator capable of resolving local wavelengths, a mesh partitioner that rapidly provides asymptotically optimal partitions, several initialization steps that are carried out prior to parallel solution of the discrete wave propagation equations, and the parallel code generator, which shields the user from issues of parallelism and communication, while allowing a high-level description of the numerical method.