An Efficient Multi-Level Fast Multipole Method Implementation on FPGA

Abstract:
Micromagnetic simulations are widely used to study the magnetization dynamics of ferromagnetic materials. A key step of the simulation is the calculation of the magnetostatic field (aka demagnetization field). To get a relatively precise estimate one needs to take the magnetostatic field into account. The magnetostatic field describes the long range interactions between magnetic dipoles. This is the most computationally intensive part of the magnetic simulation because with brute force calculations it scales with O(N²) when increasing the simulated region. By using the Fast Multipole Method the computations can be carried out by O(N log N) or in some cases O(N). In this paper we propose an FPGA implementation of the micromagnetic simulator in order to accelerate the computations. The details of the implementations are discussed along with the resulting speed, power consumption and resource requirements.