BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unconditional weak convergence to weak solutions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917262224523264 |
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| author | Aldé, Michele Feischl, Michael Praetorius, Dirk |
| author_facet | Aldé, Michele Feischl, Michael Praetorius, Dirk |
| contents | We consider the Landau-Lifshitz-Gilbert equation (LLG) that models time-dependent micromagnetic phenomena. We propose a full discretization that employs first-order finite elements in space and a BDF2-type two-step method in time. In each time step, only one linear system of equations has to be solved. We employ linear interpolation in time to reconstruct the discrete space-time magnetization. We prove that the integrator is unconditionally stable and thus guarantees that a subsequence of the reconstructed magnetization converges weakly in $H^1$ towards a weak solution of LLG in the space-time domain. Numerical experiments verify that the proposed integrator is indeed first-order in space and second-order in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unconditional weak convergence to weak solutions Aldé, Michele Feischl, Michael Praetorius, Dirk Numerical Analysis 65M12 (Primary) 35K61, 65M60, 65L06, 65Z05 (Secondary) We consider the Landau-Lifshitz-Gilbert equation (LLG) that models time-dependent micromagnetic phenomena. We propose a full discretization that employs first-order finite elements in space and a BDF2-type two-step method in time. In each time step, only one linear system of equations has to be solved. We employ linear interpolation in time to reconstruct the discrete space-time magnetization. We prove that the integrator is unconditionally stable and thus guarantees that a subsequence of the reconstructed magnetization converges weakly in $H^1$ towards a weak solution of LLG in the space-time domain. Numerical experiments verify that the proposed integrator is indeed first-order in space and second-order in time. |
| title | BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unconditional weak convergence to weak solutions |
| topic | Numerical Analysis 65M12 (Primary) 35K61, 65M60, 65L06, 65Z05 (Secondary) |
| url | https://arxiv.org/abs/2511.22000 |