Alternative Method for Making Explicit FDTD Unconditionally Stable

An alternative method is developed to make an explicit FDTD unconditionally stable. In this method, given any time step, we find the modes that cannot be stably simulated by the given time step, and deduct these modes directly from the system matrix (discretized curl-curl operator) before the explicit time marching. By doing so, the original FDTD numerical system is adapted based on the desired time step to rule out the root cause of instability. The resultant explicit FDTD marching is absolutely stable for the given time step no matter how large it is, and irrespective of space step. The accuracy is also guaranteed for time step chosen based on accuracy. Numerical experiments have validated the accuracy, efficiency, and unconditional stability of the proposed new method for making an explicit FDTD unconditionally stable.

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