The Landau-Lifshitz (LL) equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also interesting mathematical properties of the LL equation: nonlocal character for some quantities, nonconvex side-constraints, strongly nonlinear terms. These effects influence also numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions, are addressed.
The Landau-Lifshitz (LL) equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also an interesting mathematical properties of the LL equation: nonlocal character for some quantities, nonconvex sideconstraints, strongly nonlinear terms. These effects influence also the numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions, are addressed.
We review the lattice-Boltzmann (LB) method coupled with the immersed boundary (IB) method for the description of combined flow of particulate suspensions with immersed elastic objects. We describe the implementation of the combined LB-IB method into the open-source package ESPResSo. We present easy-to-use structures used to model a closed object in a simulation package, the definition of its elastic properties, and the interaction between the fluid and the immersed object. We also present the test cases with short examples of the code explaining the functionality of the new package.
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