Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime
Time dependent Schrödinger equations with conservative force field commonly constitute a major challenge in the numerical approximation, especially when they are analysed in the semiclassical regime. Extremely high oscillations originate from the semiclassical parameter, and call for appropriate met...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2019
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| _version_ | 1797075553130381312 |
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| author | Auzinger, W Hofstätter, H Koch, O Kropielnicka, K Singh, P |
| author_facet | Auzinger, W Hofstätter, H Koch, O Kropielnicka, K Singh, P |
| author_sort | Auzinger, W |
| collection | OXFORD |
| description | Time dependent Schrödinger equations with conservative force field commonly constitute a major challenge in the numerical approximation, especially when they are analysed in the semiclassical regime. Extremely high oscillations originate from the semiclassical parameter, and call for appropriate methods. We propose to employ a combination of asymptotic Zassenhaus splitting with time adaptivity. While the former turns the disadvantage of the semiclassical parameter into an advantage, leading to highly efficient methods with low error constants, the latter enables to choose an optimal time step and to speed up the calculations when the oscillations subside. We support the results with numerical examples. |
| first_indexed | 2024-03-06T23:51:56Z |
| format | Journal article |
| id | oxford-uuid:72e60721-7db5-482e-940b-9e4e9b761aab |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:51:56Z |
| publishDate | 2019 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:72e60721-7db5-482e-940b-9e4e9b761aab2022-03-26T19:53:02ZTime adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regimeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:72e60721-7db5-482e-940b-9e4e9b761aabEnglishSymplectic Elements at OxfordElsevier2019Auzinger, WHofstätter, HKoch, OKropielnicka, KSingh, PTime dependent Schrödinger equations with conservative force field commonly constitute a major challenge in the numerical approximation, especially when they are analysed in the semiclassical regime. Extremely high oscillations originate from the semiclassical parameter, and call for appropriate methods. We propose to employ a combination of asymptotic Zassenhaus splitting with time adaptivity. While the former turns the disadvantage of the semiclassical parameter into an advantage, leading to highly efficient methods with low error constants, the latter enables to choose an optimal time step and to speed up the calculations when the oscillations subside. We support the results with numerical examples. |
| spellingShingle | Auzinger, W Hofstätter, H Koch, O Kropielnicka, K Singh, P Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime |
| title | Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime |
| title_full | Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime |
| title_fullStr | Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime |
| title_full_unstemmed | Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime |
| title_short | Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime |
| title_sort | time adaptive zassenhaus splittings for the schrodinger equation in the semiclassical regime |
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