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arXiv · 2406.05489

On a class of multi-fidelity methods for the semiclassical Schr\"odinger equation with uncertainties

Yiwen Lin·Liu Liu
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Abstract

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.

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Yiwen Lin, Liu Liu. 2024-06-08. On a class of multi-fidelity methods for the semiclassical Schr\"odinger equation with uncertainties. https://arxiv.org/abs/2406.05489

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