Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current Problems
Incremental improvement for computational electromagnetics researchers seeking faster time integration in eddy current simulations.
The authors transform a stiff differential algebraic equation system into a finitely stiff ODE for transient eddy current problems, and compare subspace projection extrapolation and proper orthogonal decomposition to reduce PCG iterations for multiple right-hand sides, achieving reduced computational costs.
The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential algebraic equation system into a finitely stiff ordinary differential equation (ODE) system by application of a generalized Schur complement for nonconducting parts. The ODE can be integrated in time using explicit time integration schemes, e.g. the explicit Euler method. This requires the repeated evaluation of a pseudo-inverse of the discrete curl-curl matrix in nonconducting material by the preconditioned conjugate gradient (PCG) method which forms a multiple right-hand side problem. The subspace projection extrapolation method and proper orthogonal decomposition are compared for the computation of suitable start vectors in each time step for the PCG method which reduce the number of iterations and the overall computational costs.