Two Unconditional Stable Schemes for Simulation of Heat Equation on Manifold Using DEC

To predict the heat diffusion in a given region over time, it is often necessary to find the numerical solution for heat equation. However, the computational domain of classical numerical methods are limited to flat spacetime. With the techniques of discrete differential calculus, we propose two unconditional stable numerical schemes for simulation heat equation on space manifold and time. The analysis of their stability and error is accomplished by the use of maximum principle. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)