Simple recursive implementation of fast multipole method

Visscher, P. B.; Apalkov, Dmytro

doi:10.1016/j.jmmm.2009.09.033

Cited by 23 publications

(28 citation statements)

References 22 publications

(31 reference statements)

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“…Finally, there is another possibility of vortex conversion into the uniform in-plane state, not captured by the expression (13). At very small thicknesses the vortex may become unstable with respect to lateral shift.…”

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confidence: 99%

“…Magnetism@home project numerically computed magnetostatic energy (including that of volume, face and side magnetic charges, as well as their mutual interaction) of magnetization distributions (1) in a 4-dimensional unithypercube with normalized coordinates g = g/(1 + g), c = c/(1 + c), a = a/(1 + a), p = 1/p, which covers all the magnetization configurations it describes. The densities of magnetic charges were computed analytically, while the magnetostatic energy itself was evaluated using fast multipole method [13] on a dense 50000 non-uniform finite elements mesh, perfectly covering the circular cylinder's boundary, with exact analytical treatment for Z dependence of demagnetizing field. This computation (including preliminary testing runs) took about a year to complete, using idle processor time of a several tens of thousands of computers on the Internet, communicating via Berkeley Open Infrastructure for Network Computing (BOINC) protocol.…”

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confidence: 99%

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Equilibrium large vortex state in ferromagnetic disks

Metlov

2013

Journal of Applied Physics

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Magnetic vortices in soft ferromagnetic nano-disks have been extensively studied for at least several decades both for their fundamental (as a "live" macroscopic realization of a field theory model of an elementary particle) as well as applied value for high-speed high-density power-independent information storage. Here it is shown that there is another vortex state in nano-scale ferromagnetic disks of several exchange lengths in size. The energy of this large vortex state is computed numerically (within the framework of Magnetism@home distributed computing project) and its stability is studied analytically, which allows to plot it on magnetic phase diagram. It is the ground state of cylinders of certain sizes and is metastable in a wider set of geometries. Large vortices exist on par with classical ones, while being separated by an energy barrier, controllable by tuning the geometry and material of ferromagnetic disk. This state can be an excellent candidate for magnetic information storage not only because the resulting disk sizes are among the smallest, able to support magnetic vortices, but also because it is the closest to the classical vortex state of all other known metastable states of magnetic nano-cylinder, which implies, that the memory, based on switching between these two different types of magnetic vortices, may, potentially, achieve the highest possible rate of switching. [5], including the remarkable results on switching the vortex core polarity by ultrashort in-plane magnetic field pulses[6-8]. However, despite the driving pulses can be made extremely short, the switching itself is usually accompanied by much longer magnetization dynamics during which the new equilibrium state is established [9]. If the switching process involves creation of additional vortices and anti-vortices, they must be annihilated at the end, which implies significant spin-wave generation [10]. The energy of these spin-waves (as well as other energy, accumulated by magnetization) must be dissipated, which limits the sustained rate of switching of such a devices. This limitation is more pronounced, the longer is the trajectory, each spin must pass during the switching, or, the bigger is the distance between the metastable states used. Knowing these states is, therefore, very important for applications and also is an intriguing fundamental problem. Similarity of the equations means that finding a new metastable state in nano-magnetism is like discovering a new elementary particle in non-linear field theory. With a difference that nano-magnets have boundary, allowing for existence of additional states, such as boundary-bound half-vortices and anti-vortices[11] as well as large vortices.Because the equations for equilibrium magnetic textures are non-linear and non-local, solving them for stationary states usually involves significant guesswork. Usually, new states (such as domain structures or new types of domain walls) are first observed in experiments (or numerical experiments) and only then described theoretically. The ex...

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Equilibrium large vortex state in ferromagnetic disks

Metlov

2013

Journal of Applied Physics

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“…Over the 25 years of its existence, the FMM underwent several changes and improvements in order to reduce the complexity coefficients, make it practical in 3D, apply it to various kernels, using different expansions, and using different data structures and spatial adaptivity to reduce the amount of work needed [11][12][13]. Also, the implementation of the FMM saw many advances from sequential to massively parallel, and optimizations on heterogeneous CPU-GPU platforms [14][15][16].…”

Section: The Fast Multipole Methodsmentioning

confidence: 99%

The fast multipole method for N-body problems

Erdelyi¹

2013

AIP Conference Proceedings

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“…From a source point (or field point, resp.) perspective the truncation error is proportional to (α/2) p+1 where α is the opening angle 2r/d with r being the diameter of source (or field) cell and d the distance between centers [21]. Plugging the expansion into the expression for the j-th volume source (eq.…”

Section: Source Expansionmentioning

confidence: 99%

Highly parallel demagnetization field calculation using the fast multipole method on tetrahedral meshes with continuous sources

Palmesi

Exl

Bruckner

et al. 2017

Journal of Magnetism and Magnetic Materials

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The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Improvements both on a numerical and computational basis can relief problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. We assume linearly magnetized tetrahedral sources, treat the near field directly and use analytical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory.

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Simple recursive implementation of fast multipole method

Cited by 23 publications

References 22 publications

Equilibrium large vortex state in ferromagnetic disks

Equilibrium large vortex state in ferromagnetic disks

The fast multipole method for N-body problems

Highly parallel demagnetization field calculation using the fast multipole method on tetrahedral meshes with continuous sources

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