Parallelisation of micromagnetic simulations

Abstract

The field of paleomagnetism attempts to understand in detail the the processes of the Earth by studying naturally occurring magnetic samples. These samples are quite unlike those fabricated in the laboratory. They have irregular shapes; they have been squeezed and stretched, heated and cooled and subjected to oxidation. However micromagnetic modelling allows us to simulate such samples and gain some understanding of how a paleomagnetic signal is acquired and how it is retained. Micromagnetics provides a theory for understanding how the domain structure of a magnetic sample alters subject to what it is made from and the environment that it is in. It furnishes the mathematics that describe the energy of a given domain structure and how that domain structure evolves in time. Combining micromagnetics and ever increasing computer power, it has been possible to produce simulations of small to medium size grains within the so-called single to pseudo single domain state range. However processors are no longer built with increasing speed but with increasing parallelism and it is this that must be exploited to model larger and larger paleomagnetic samples. The purpose of the work presented here is twofold. Firstly a micromagnetics code that is parallel and scalable is presented. This code is based on FEniCS, an existing finite element framework, and is shown to run on ARCHER the UK’s national supercomputing service. The strategy of using existing libraries and frameworks allow future extension and inclusion of new science in the code base. In order to achieve scalability, a spatial mapping technique is used to calculate the demagnetising field - the most computationally intensive part of micromagnetic calculations. This allows grain geometries to be partitioned in such a way that no global communication is required between parallel processes - the source of favourable scaling behaviour. The second part of the theses presents an exploration of domain state evolution in increasing sizes of magnetite grains. This simulation, whilst a first approximation that excludes magneto-elastic effects, is the first attempt to map out the transition from pseudo-single domain states to multi domain states using a full micromagnetic simulation.