Hybrid Superposition Integral—Poisson Solver Method for the Magnetostatic Field in Finite Element Micromagnetic Solvers

A hybrid integral evaluation—differential equation approach is introduced for the computation of the magnetostatic fields in finite-element method (FEM)-based micromagnetic solvers. The approach calculates the magnetostatic field at the boundary of the computational domain or any additional surfaces by direct superposition via a fast approach, such as the adaptive integral method based on the fast Fourier transform (FFT), and uses this surface values to formulate a Poisson equation problem with Dirichlet boundary conditions to compute the field in the bulk of the structure. The benefits of this hybrid approach include a significant reduction of the sparse matrices used in the accurate integral evaluation with the associated memory reduction as well as a rapidly convergent Poisson solver without a need of significantly extending the domain size. Additional benefits include the ability to subdivide the problem into a set of smaller problems with multiple Poisson problems for parallelization.