Numerical Analysis of Multi-patch Discontinuous Galerkin Isogeometric Method for Full-potential Electronic Structure Calculations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917867914526720 |
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| author | Li, Xiaoxu Meng, Xucheng |
| author_facet | Li, Xiaoxu Meng, Xucheng |
| contents | In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the wavefunction separately using B-spline basis functions, possibly with different degrees, on varying mesh sizes, and then combine them by DG methods. We also provide a rigorous {\em a priori} error analysis of the DG-IGA approximations for linear eigenvalue problems. Furthermore, this work offers a unified analysis framework for the DG-IGA method applied to a class of elliptic eigenvalue problems. Finally, we present several numerical experiments to verify our theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Analysis of Multi-patch Discontinuous Galerkin Isogeometric Method for Full-potential Electronic Structure Calculations Li, Xiaoxu Meng, Xucheng Numerical Analysis In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the wavefunction separately using B-spline basis functions, possibly with different degrees, on varying mesh sizes, and then combine them by DG methods. We also provide a rigorous {\em a priori} error analysis of the DG-IGA approximations for linear eigenvalue problems. Furthermore, this work offers a unified analysis framework for the DG-IGA method applied to a class of elliptic eigenvalue problems. Finally, we present several numerical experiments to verify our theoretical results. |
| title | Numerical Analysis of Multi-patch Discontinuous Galerkin Isogeometric Method for Full-potential Electronic Structure Calculations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.10045 |