Three-dimensional (3-D) basinwide simulation of generation, migration, and accumulation of hydrocarbons has vast potential as an uncertainty- and risk-assessment tool in petroleum exploration. To fulfill this potential, several challenges have to be addressed, including the realistic modeling of the evolution of complex geologic structures such as salt diapirs and fault motion. In this chapter, we describe a novel architecture that we have designed and implemented, which specifically addresses technical challenges such as 3-D representation of geologic models, meshing, parallel computing, and visualization of the massive amount of data involved in these simulations. The core of this architecture is a 3-D topological framework for the representation of evolving geologic structures. This enables numeric simulation of geologic processes undergoing large deformations in sedimentary basin and lithosphere. In this framework, the topology (or informally, connectivity) is separated from the geometry of the geologic models, making it possible to update the geometry without altering the model topology. A mesh is treated as a possible realization of the geometric model and hence as an attribute of the topology. This architecture greatly facilitates the automatic meshing and remeshing required for large deformations such as those associated with the formation and evolution of salt diapirs. In addition, this architecture was designed to consider the geometry of geologic elements in the partitioning of the computational domain, and thus, it is suitable to the solution of partial differential equations in parallel. This is beneficial because of the large computational resources required to solve numerically the equations governing heat and fluid-transport processes in sediments.