Fast computational methods for large-scale eddy-current computation

In this paper, we present a technique for solving large-scale problems arising from the discretization of an integral formulation for three-dimensional eddy current problems in the magnetoquasi-static limit using edge-element-based shape functions. The proposed approach is in the framework of the precorrected fast Fourier transform method (PFFTM) that allows to compute the product of the full stiffness matrix with a vector in O(N log N) operations. A key point of standard PFFTM is the introduction of point-like sources defined onto a regular grid to approximate an arbitrary current density in the conductor and to compute the large distance interactions by FFT. Point-like sources are not suitable for representing solenoidal current densities as required for eddy currents problems. In this paper, edge-element-based shape functions onto the regular grid are introduced instead of the point-like sources. This allows us to improve the approximation (solenoidal current densities are approximated by solenoidal basis functions) and to reduce further the computational cost.