On a class of multi-fidelity methods for the semiclassical Schr\"odinger equation with uncertainties
<|reference_start|>On a class of multi-fidelity methods for the semiclassical Schr\"odinger equation with uncertainties: In this paper, we study the semiclassical Schr\"odinger equation with random parameters and develop several robust multi-fidelity methods. We employ the time-splitting Fourier pseudospectral (TSFP) method for the high-fidelity solver, and consider different low-fidelity solvers including the meshless method like frozen Gaussian approximation (FGA) and the level set (LS) method for the semiclassical limit of the Schr\"odinger equation. With a careful choice of the low-fidelity model, we obtain an error estimate for the bi-fidelity method. We conduct numerous numerical experiments and validate the accuracy and efficiency of our proposed multi-fidelity methods, by comparing the performance of a class of bi-fidelity and tri-fidelity approximations.<|reference_end|>
@article{lin2024on,
    title={On a class of multi-fidelity methods for the semiclassical Schr\"odinger
  equation with uncertainties},
    author={Yiwen Lin and Liu Liu},
    journal={arXiv preprint arXiv:2406.05489},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05489},
    primaryClass={math.NA cs.NA}
}