191 research outputs found
Computation of the magnetostatic interaction between linearly magnetized polyhedrons
In this paper we present a method to accurately compute the energy of the
magnetostatic interaction between linearly (or uniformly, as a special case)
magnetized polyhedrons. The method has applications in finite element
micromagnetics, or more generally in computing the magnetostatic interaction
when the magnetization is represented using the finite element method (FEM).
The magnetostatic energy is described by a six-fold integral that is singular
when the interaction regions overlap, making direct numerical evaluation
problematic. To resolve the singularity, we evaluate four of the six iterated
integrals analytically resulting in a 2d integral over the surface of a
polyhedron, which is nonsingular and can be integrated numerically. This
provides a more accurate and efficient way of computing the magnetostatic
energy integral compared to existing approaches.
The method was developed to facilitate the evaluation of the demagnetizing
interaction between neighouring elements in finite-element micromagnetics and
provides a possibility to compute the demagnetizing field using efficient fast
multipole or tree code algorithms
Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration
In the finite difference method which is commonly used in computational
micromagnetics, the demagnetizing field is usually computed as a convolution of
the magnetization vector field with the demagnetizing tensor that describes the
magnetostatic field of a cuboidal cell with constant magnetization. An
analytical expression for the demagnetizing tensor is available, however at
distances far from the cuboidal cell, the numerical evaluation of the
analytical expression can be very inaccurate.
Due to this large-distance inaccuracy numerical packages such as OOMMF
compute the demagnetizing tensor using the explicit formula at distances close
to the originating cell, but at distances far from the originating cell a
formula based on an asymptotic expansion has to be used. In this work, we
describe a method to calculate the demagnetizing field by numerical evaluation
of the multidimensional integral in the demagnetization tensor terms using a
sparse grid integration scheme. This method improves the accuracy of
computation at intermediate distances from the origin.
We compute and report the accuracy of (i) the numerical evaluation of the
exact tensor expression which is best for short distances, (ii) the asymptotic
expansion best suited for large distances, and (iii) the new method based on
numerical integration, which is superior to methods (i) and (ii) for
intermediate distances. For all three methods, we show the measurements of
accuracy and execution time as a function of distance, for calculations using
single precision (4-byte) and double precision (8-byte) floating point
arithmetic. We make recommendations for the choice of scheme order and
integrating coefficients for the numerical integration method (iii)
Nmag micromagnetic simulation tool - software engineering lessons learned
We review design and development decisions and their impact for the open
source code Nmag from a software engineering in computational science point of
view. We summarise lessons learned and recommendations for future computational
science projects. Key lessons include that encapsulating the simulation
functionality in a library of a general purpose language, here Python, provides
great flexibility in using the software. The choice of Python for the top-level
user interface was very well received by users from the science and engineering
community. The from-source installation in which required external libraries
and dependencies are compiled from a tarball was remarkably robust. In places,
the code is a lot more ambitious than necessary, which introduces unnecessary
complexity and reduces main- tainability. Tests distributed with the package
are useful, although more unit tests and continuous integration would have been
desirable. The detailed documentation, together with a tutorial for the usage
of the system, was perceived as one of its main strengths by the community.Comment: 7 pages, 5 figures, Software Engineering for Science, ICSE201
Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors
It was recently proposed to use the stray magnetic fields of superconducting
vortex lattices to trap ultracold atoms for building quantum emulators. This
calls for new methods for engineering and manipulating of the vortex states.
One of the possible routes utilizes type-1.5 superconducting layered systems
with multi-scale inter-vortex interactions. In order to explore the possible
vortex states that can be engineered, we present two phase diagrams of
phenomenological vortex matter models with multi-scale inter-vortex
interactions featuring several attractive and repulsive length scales. The
phase diagrams exhibit a plethora of phases, including conventional 2D lattice
phases, five stripe phases, dimer, trimer, and tetramer phases, void phases,
and stable low-temperature disordered phases. The transitions between these
states can be controlled by the value of an applied external field.Comment: 16 pages, 20 figure
Vortex matter in layered superconductors without Josephson coupling: numerical simulations within a mean-field approach
We study vortex matter in layered superconductors in the limit of zero Josephson coupling. The long range of the interaction between pancake vortices in the c direction allows us to employ a mean-field method: all attractive interlayer interactions are reduced to an effective substrate potential, which pancakes experience in addition to the same-layer pancake repulsion. We perform numerical simulations of this mean-field model using two independent numerical implementations with different simulation methods (Monte Carlo sampling and Langevin molecular dynamics). The substrate potential is updated self-consistently from the averaged pancake density. Depending on temperature, this potential converges to a periodic profile (crystal) or vanishes (liquid). We compute thermodynamic properties of the system, such as the melting line, the instability line of the crystal, and the entropy jump across the melting transition. The simulation results are in good agreement with approximate analytical calculations
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