We exploit notation of discrete exterior calculus (DEC)

Fields are replicated with discrete p-forms, which

• consist of values integrated over each p-cell

Grad, curl, and div are replaced with discrete exterior derivatives, which

• exactly fulfills Stokes' theorem
• can be adapted to any dimension

Material or metric is included in discrete Hodge star, which

• include all error sources
• is a diagonal matrix (when using orthogonal duality)

For details, see our presentation.

The main focus is on time-integration of wave equations. With DEC, the wave equations are expressed in a way that the "discrete energy" conserves during the time-integration. See the Online time integrator, where you can play with two-dimensional wave in real time.