Fractured meshes

This work introduces “generalized meshes”, a type of meshes suited for the discretization partial differential equations in non-regular geometries. Generalized extend regular simplicial by allowing overlapping elements and more flexible adjacency relations. They can have several distinct “generalized” vertices (or edges, faces) that occupy same geometric position. These generalized facets are natural degrees freedom classical conforming spaces discrete forms appearing finite boundary element applications. Special attention is devoted to representation fractured domains their boundaries. An algorithm proposed construct so-called virtually inflated mesh, which correspond “two-sided” mesh fracture. Discrete d-differential on characterized as trace space surrounding volume.