The focus of this talk is not a result of a calculation but a tool to model partial differential equations. The tool is what we call discrete exterior calculus (DEC). Simplex-based DEC is similar to vector calculus. (Vertices, edges, triangles and tetrahedrons are simplices.) I will first review how DEC is built and how it relates to the standard vector calculus. I will then introduce the simplicial homology group (or betti group) and show the relation to the vector Laplace equation. As an example of the use of DEC, I will present the solution of the time-dependent Gross-Pitaevskii equation (Schroedinger-like equation with nonlinear terms) on a toroidal surface with a hole.