Report
A posteriori error estimates for Schrödinger operators discretized with linear combinations of atomic orbitals
| العنوان: | A posteriori error estimates for Schrödinger operators discretized with linear combinations of atomic orbitals |
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| المؤلفون: | Dusson, Geneviève, Dupuy, Mi-Song, Lygatsika, Ioanna-Maria |
| المساهمون: | Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté COMUE (UBFC)-Université Bourgogne Franche-Comté COMUE (UBFC), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), CEA/DAM Arpajon (CEA/DAM), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), ANR-15-IDEX-0003,BFC,ISITE " BFC(2015), European Project: 810367,EMC2(2019) |
| المصدر: | https://hal.science/hal-04723742 ; 2024. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | A posteriori analysis Eigenvalue problem Localized basis set Schrödinger equation MSC codes. 35Q40 65N15 65N25, A posteriori analysis, Eigenvalue problem, Localized basis set, Schrödinger equation MSC codes. 35Q40, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| الوصف: | We establish guaranteed and practically computable a posteriori error bounds for source problems and eigenvalue problems involving linear Schrödinger operators with atom-centered potentials discretized with linear combinations of atomic orbitals. We show that the energy norm of the discretization error can be estimated by the dual energy norm of the residual, that further decomposes into atomic contributions, characterizing the error localized on atoms. Moreover, we show that the practical computation of the dual norms of atomic residuals involves diagonalizing radial Schrödinger operators which can easily be precomputed in practice. We provide numerical illustrations of the performance of such a posteriori analysis on several test cases, showing that the error bounds accurately estimate the error, and that the localized error components allow for optimized adaptive basis sets. |
| نوع الوثيقة: | report |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/2410.04943; info:eu-repo/grantAgreement//810367/EU/Extreme-Scale Mathematically-based Computational Chemistry/EMC2; ARXIV: 2410.04943 |
| الاتاحة: | https://hal.science/hal-04723742 https://hal.science/hal-04723742v1/document https://hal.science/hal-04723742v1/file/papier.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.413ED559 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |