Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current Problems

TL;DR

This paper explores efficient explicit time integration techniques for transient eddy current problems by comparing methods to improve the computation of multiple right-hand sides in iterative solvers, reducing computational costs.

Contribution

It introduces and compares subspace projection extrapolation and proper orthogonal decomposition for improving PCG solver efficiency in semi-explicit time integration methods.

Findings

Subspace projection extrapolation reduces PCG iterations.

Proper orthogonal decomposition improves initial guess quality.

Overall computational costs are decreased with these methods.

Abstract

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.