Fast Explicit Diffusion (FED) is a simple explicit scheme that uses varying time step sizes [1]. It is substantially faster than usual explicit schemes: Up to 50% of its time step sizes exceed the stability limit, and the stopping time grows quadratically in the number of steps. Thus, a few steps suffice to obtain astonishing stopping times. Another advantage of FED is the simplicity of implementation. Any explicit scheme can easily be converted into FED by adding two simple precomputation steps: Deriving the time step sizes, and choosing a suitable rearrangement in order to tame rounding errors. Besides being very efficient on sequential hardware, FED is also very well suited for massively parallel architectures, such as GPUs. Due to its simplicity, even complex diffusion-like processes such as highly accurate optic flow methods can easily be realised [2]. The resulting algorithms for GPUs beat the most sophisticated numerical solvers on CPUs by two to three orders of magnitude.
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