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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.05489 |
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| _version_ | 1866911106389245952 |
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| author | Lin, Yiwen Liu, Liu |
| author_facet | Lin, Yiwen Liu, Liu |
| contents | In this paper, we study the semiclassical Schrödinger 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 Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a class of multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties Lin, Yiwen Liu, Liu Numerical Analysis 35J10, 65M70 In this paper, we study the semiclassical Schrödinger 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 Schrödinger 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. |
| title | On a class of multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties |
| topic | Numerical Analysis 35J10, 65M70 |
| url | https://arxiv.org/abs/2406.05489 |