Computational Electromagnetism and Implicit Discrete Exterior Calculus

The implicit Euler scheme of time variable and discrete exterior calculus can be united to find an unconditional stable approach, which is called implicit discrete exterior calculus. This technique for solving Maxwell’s equations in time domain is discussed, which provides flexibility in numerical computing on manifold. For some problems, it takes much less computational time to use the implicit method with larger time steps, even taking into account that one needs to solve equations at each step. This algorithm has been implemented on Java development plateform for simulating TE/M waves in vacuum.