A discrete-exterior-calculus beam propagation method accelerates nonlinear Schrödinger equation simulations on step-index fibers by ~73-150x relative to an FFT spectral solver, but it is second-order convergent, not spectral.
N.Spectral Methods in MATLAB(SIAM, 2000)
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A 100x Faster Beam Propagation Method for Nonlinear Optical Wave Propagation Based on Discrete Exterior Calculus
A discrete-exterior-calculus beam propagation method accelerates nonlinear Schrödinger equation simulations on step-index fibers by ~73-150x relative to an FFT spectral solver, but it is second-order convergent, not spectral.