Multiple right-hand side techniques for the numerical simulation of quasistatic electric and magnetic fields

The simulation of slowly varying transient electric high-voltage fields and magnetic fields requires the repeated and successive solution of high-dimensional linear algebraic systems of equations with identical or near-identical system matrices and different right-hand side vectors. For these solution processes which are required within implicit time integration schemes and nonlinear (quasi-)Newton–Raphson methods an iterative multiple right-hand side (mrhs) scheme is used which recycles vector subspaces resulting from previous preconditioned conjugate gradient iteration runs. The combination of this scheme with a subspace projection extrapolation start value generation scheme is discussed. Numerical results for three-dimensional electric and magnetic field simulations are presented and the efficiency of the new schemes re-using eigenvector information from previous iteration processes with different tolerance criteria are compared to those of standard conjugate gradient iterations.