Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3
Thermal fluctuations play an increasingly important role in micromagnetic research relevant for various biomedical and other technological applications. Until now, it was deemed necessary to use a time stepping algorithm with a fixed time step in order to perform micromagnetic simulations at nonzero...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2017-12-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.5003957 |
| _version_ | 1818032942848409600 |
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| author | J. Leliaert J. Mulkers J. De Clercq A. Coene M. Dvornik B. Van Waeyenberge |
| author_facet | J. Leliaert J. Mulkers J. De Clercq A. Coene M. Dvornik B. Van Waeyenberge |
| author_sort | J. Leliaert |
| collection | DOAJ |
| description | Thermal fluctuations play an increasingly important role in micromagnetic research relevant for various biomedical and other technological applications. Until now, it was deemed necessary to use a time stepping algorithm with a fixed time step in order to perform micromagnetic simulations at nonzero temperatures. However, Berkov and Gorn have shown in [D. Berkov and N. Gorn, J. Phys.: Condens. Matter,14, L281, 2002] that the drift term which generally appears when solving stochastic differential equations can only influence the length of the magnetization. This quantity is however fixed in the case of the stochastic Landau-Lifshitz-Gilbert equation. In this paper, we exploit this fact to straightforwardly extend existing high order solvers with an adaptive time stepping algorithm. We implemented the presented methods in the freely available GPU-accelerated micromagnetic software package MuMax3 and used it to extensively validate the presented methods. Next to the advantage of having control over the error tolerance, we report a twenty fold speedup without a loss of accuracy, when using the presented methods as compared to the hereto best practice of using Heun’s solver with a small fixed time step. |
| first_indexed | 2024-12-10T06:15:23Z |
| format | Article |
| id | doaj.art-c16967124d064682b8a2e220b79877b3 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-10T06:15:23Z |
| publishDate | 2017-12-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-c16967124d064682b8a2e220b79877b32022-12-22T01:59:28ZengAIP Publishing LLCAIP Advances2158-32262017-12-01712125010125010-1310.1063/1.5003957017712ADVAdaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3J. Leliaert0J. Mulkers1J. De Clercq2A. Coene3M. Dvornik4B. Van Waeyenberge5Department of Solid State Sciences, Ghent University, 9000 Gent, BelgiumDepartment of Solid State Sciences, Ghent University, 9000 Gent, BelgiumDepartment of Solid State Sciences, Ghent University, 9000 Gent, BelgiumDepartment of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, 9052 Zwijnaarde, BelgiumDepartment of Physics, University of Gothenburg, 412 96, Gothenburg, SwedenDepartment of Solid State Sciences, Ghent University, 9000 Gent, BelgiumThermal fluctuations play an increasingly important role in micromagnetic research relevant for various biomedical and other technological applications. Until now, it was deemed necessary to use a time stepping algorithm with a fixed time step in order to perform micromagnetic simulations at nonzero temperatures. However, Berkov and Gorn have shown in [D. Berkov and N. Gorn, J. Phys.: Condens. Matter,14, L281, 2002] that the drift term which generally appears when solving stochastic differential equations can only influence the length of the magnetization. This quantity is however fixed in the case of the stochastic Landau-Lifshitz-Gilbert equation. In this paper, we exploit this fact to straightforwardly extend existing high order solvers with an adaptive time stepping algorithm. We implemented the presented methods in the freely available GPU-accelerated micromagnetic software package MuMax3 and used it to extensively validate the presented methods. Next to the advantage of having control over the error tolerance, we report a twenty fold speedup without a loss of accuracy, when using the presented methods as compared to the hereto best practice of using Heun’s solver with a small fixed time step.http://dx.doi.org/10.1063/1.5003957 |
| spellingShingle | J. Leliaert J. Mulkers J. De Clercq A. Coene M. Dvornik B. Van Waeyenberge Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3 AIP Advances |
| title | Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3 |
| title_full | Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3 |
| title_fullStr | Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3 |
| title_full_unstemmed | Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3 |
| title_short | Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3 |
| title_sort | adaptively time stepping the stochastic landau lifshitz gilbert equation at nonzero temperature implementation and validation in mumax3 |
| url | http://dx.doi.org/10.1063/1.5003957 |
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