Full multigrid for magnetostatics using unstructured and non-nested meshes

Abstract

Adaptive mesh refinement and mesh enhancing techniques, commonly applied in electromagnetic finite element simulation, give raise to a hierarchy of nonnested unstructured grids. The application of geometrical multigrid is not straightforward. The prolongation operator is adapted to the particular properties of the mesh refinement. Anti-symmetric boundary conditions and nonlinear material characteristics are incorporated. The numerical experiment performed on the model of a synchronous machine shows optimal convergence for the proposed multigrid scheme whereas the convergence of classical nested multigrid becomes troublesome.Index Terms-Adaptive mesh refinement, finite element methods, iterative solvers, multigrid methods.

Fast Fourier transform on multipoles for rapid calculation of magnetostatic fields

“…Recent developments in this approach saw implementations of the fast algorithms, such as the tree-code [26] and FFTM [27], to speed up the calculations of the dense-matrix-vector product. It is also worth mentioning that the multigrid methods [28]- [30] were also employed to improve the convergence of the iterative solver when solving the boundary value problems with FEM.…”