A parallel-in-time solver for nonlinear degenerate time-periodic parabolic problems

TL;DR

This paper introduces a parallel-in-time iterative solver for nonlinear degenerate time-periodic parabolic problems, demonstrating efficiency and convergence independence from discretization parameters, validated through power transformer simulations.

Contribution

The paper presents a novel parallel-in-time fixed-point iteration method with proven global convergence for nonlinear time-periodic problems, applicable to electrical engineering simulations.

Findings

Global convergence with contraction factors independent of discretization

Efficient solution of power transformer simulation problems

Comparison shows improved performance over existing methods

Abstract

A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based on a fixed-point iteration. Every step of this iteration amounts to the solution of a discretized time-periodic and time-invariant problem for which efficient parallel-in-time methods are available. Global convergence with contraction factors independent of the discretization parameters is established. Together with an appropriate initialization step, a highly efficient and reliable solver is obtained. The applicability and performance of the proposed method is illustrated by simulations of a power transformer. Further comparison is made with other solution strategies proposed in the literature.