In this section we discuss the numerical and geometric algorithms necessary for modeling earthquake-induced ground motion in large, heterogeneous basins. In the next three subsections, we briefly discuss a mesh generation technique capable of resolving local wavelengths, a mesh partitioner that rapidly provides asymptotically optimal partitions, and several initialization steps that are carried out prior to parallel solution of the discrete wave propagation equations. The last subsection provides the governing equations and overviews spatial and temporal discretization strategies appropriate for distributed memory parallel computers.