An algorithm is introduced for converting a non-conforming hexahedral mesh that is topologically equivalent and geometrically similar to a given geometry into a conforming mesh for the geometry. The procedure involves embedding geometric topology information into the given non-conforming base mesh and then converting the mesh to a fundamental hexahedral mesh. The procedure is extensible to multi-volume meshes with minor modification, and can also be utilized in a geometry-tolerant form (i.e.,

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... wanted features within a solid geometry can be ignored with minor penalty). Utilizing an octree-type algorithm for producing the base mesh, it may be possible to show asymptotic convergence to a guaranteed closure state for meshes within the geometry, and because of the prevalence of these types of algorithms in parallel systems, the algorithm should be extensible to a parallel version with minor modification.