A robust, CAD based, highly accurate and fast Cartesian mesh generation technique for a colossal number of cells capacity using a minimal single processor computing resource is presented. The cells are generated in Yee format for the Finite Difference Time Domain method. There are three key techniques presented that achieve this capability: a memory efficient ray tracing method, a highly accurate ray-facet intersection test, and a novel exact arithmetic tie-breaking algorithm for rays intersecting facet edges and vertices.