A finite element based heterogeneous multiscale method for the Landau-Lifshitz equation
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation correspond...
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| Vydáno v: | Journal of computational physics Ročník 486; s. 112112 |
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| Médium: | Journal Article |
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01.08.2023
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| ISSN: | 0021-9991, 1090-2716, 1090-2716 |
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| Abstract | We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation corresponding to the original problem. This makes it possible to obtain effective solutions to problems with rapid material variations on a small scale, described by ε≪1, which would be too expensive to resolve in a conventional simulation.
•Numerical homogenization using Heterogeneous Multiscale Methods.•Implementation of a new multiscale approach for the Landau-Lifshitz equation.•Finite element discretized macro model for flexibility.•Efficient finite difference micro model.•Makes it possible to treat arbitrarily small material variations. |
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| AbstractList | We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation corresponding to the original problem. This makes it possible to obtain effective solutions to problems with rapid material variations on a small scale, described by ε << 1, which would be too expensive to resolve in a conventional simulation. We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation corresponding to the original problem. This makes it possible to obtain effective solutions to problems with rapid material variations on a small scale, described by ε≪1, which would be too expensive to resolve in a conventional simulation. We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation corresponding to the original problem. This makes it possible to obtain effective solutions to problems with rapid material variations on a small scale, described by ε≪1, which would be too expensive to resolve in a conventional simulation. •Numerical homogenization using Heterogeneous Multiscale Methods.•Implementation of a new multiscale approach for the Landau-Lifshitz equation.•Finite element discretized macro model for flexibility.•Efficient finite difference micro model.•Makes it possible to treat arbitrarily small material variations. |
| ArticleNumber | 112112 |
| Author | Leitenmaier, Lena Nazarov, Murtazo |
| Author_xml | – sequence: 1 givenname: Lena orcidid: 0000-0003-2348-1479 surname: Leitenmaier fullname: Leitenmaier, Lena email: lenalei@kth.se organization: Department of Mathematics, KTH, Royal Institute of Technology, Lindstedsvägen 25, 10044, Stockholm, Sweden – sequence: 2 givenname: Murtazo orcidid: 0000-0003-4962-9048 surname: Nazarov fullname: Nazarov, Murtazo email: murtazo.nazarov@it.uu.se organization: Division of Scientific Computing, Department of Information Technology, Uppsala University, Lägerhyddsvägen 2, 752 37, Uppsala, Sweden |
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| Title | A finite element based heterogeneous multiscale method for the Landau-Lifshitz equation |
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