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

Abstract

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.

Convergence of highly parallel stray field calculation using the fast multipole method on irregular meshes

“…Compare Palmesi et al 2 for a deeper performance analysis. Figures 2 and 3 show a decreasing error for larger meshes.…”

“…2 The FMM splits the problem into two parts. An analytic near-or direct field and a multipole approximation for the far-field.…”

“…In Palmesi et al 2 Equation (1) has been solved directly for each cell using Graglia, 3 leading to-potentially large-canceling surface contributions inside the mesh. The multipole error is dependent on the absolute value of the integral Equation (1) making the direct solution suboptimal.…”

“…In Equations (2) and (3) field and potential have been split into surface ∂Ω i and volume Ω i terms forgoing this problem. 2 The modified version used here requires six new subprograms. Four calculate the analytic surface and volume contributions of resp.…”

MagTense: A micromagnetic framework using the analytical demagnetization tensor

“…Of these it is the calculation of the demagnetization field, also known as the stray field, that is the most time consuming part Abert et al [2013]. There are in general three methods that have been applied to calculate the demagnetization field: finite difference based fast Fourier transform methods, tensor-grid methods and finite-element methods, although other methods such as fast multipole methods also exist Van de Wiele et al [2008]; Palmesi et al [2017]; Kumar and Adeyeye [2017]. All methods have inherent advantages and shortcomings.…”