A multivector data structure for differential forms and equations Original Research Article

We use tools from algebraic topology to show that a class of structural differential equations may be represented combinatorially, and thus, by a computer data structure. In particular, every differential k-form may be represented by a formal k-cochain over a cellular structure that we call a starplex, and exterior differentiation is equivalent to the coboundary operation on the corresponding k-cochain. Furthermore, there is a one-to-one correspondence between this model and the classical finite cellular model supported by the Generalized Stokes’ Theorem and translation between the two models can be completely automated.