رسالة جامعية
Conservative high order collocation methods for nonlinear Schrödinger equations
| العنوان: | Conservative high order collocation methods for nonlinear Schrödinger equations |
|---|---|
| المؤلفون: | Riera, Pau |
| بيانات النشر: | Stockholms universitet, Fysikum; KTH Royal Institute of Technology, 2021. |
| سنة النشر: | 2021 |
| المجموعة: | DiVA Archive at Upsalla University |
| مصطلحات موضوعية: | Gross-Pitaevskii equation, Computational Mathematics, Beräkningsmatematik |
| الوصف: | In this thesis, we investigate the numerical solution of time-dependent nonlinear Schrödinger equations (more specifically, the Gross-Pitaevskii equation) that appear in the modeling of Bose-Einstein condensates. Since the model is known to conserve important physical invariants, such as mass and energy of the condensate, our goal is to study the importance of reproducing the conservation on the discrete level. The reliability of conservative, compared to non-conservative, methods shall be studied through high order collocation methods for the time discretization and finite element-based space discretizations. In particular, this includes symplectic discontinuous Galerkin time-stepping methods, as well as Continuous Petrov-Galerkin methods. The methods shall be tested for a problem with a known analytical solution, namely two interacting solitons in 1D. This problem is a suitable choice due to its high sensitivity to oscillations of the energy and difficulty to approximate for large time scales. |
| Original Identifier: | oai:DiVA.org:su-194703 |
| نوع الوثيقة: | Student thesis bachelorThesis text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| الإتاحة: | http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-194703Test |
| حقوق: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsndl.UPSALLA1.oai.DiVA.org.su.194703 |
| قاعدة البيانات: | Networked Digital Library of Theses & Dissertations |
| الوصف غير متاح. |