On a Class of Multifidelity Methods for the Semiclassical Schrödinger Equation with Uncertainties

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Abstract. In this paper, we study the semiclassical Schrödinger equation with random parameters and develop several robust multifidelity 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 of frozen Gaussian approximation (FGA) and the level set (LS) method for the semiclassical limit of the Schrödinger equation. With a careful choice of the low-fidelity model, we obtain an error estimate for the bifidelity method. We conduct numerous numerical experiments and validate the accuracy and efficiency of our proposed multifidelity methods by comparing their performance to that of a class of bifidelity and tri-fidelity approximations.

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