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arXiv · 2502.21013

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

Herbert Egger·Andreas Schafelner
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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.

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Herbert Egger, Andreas Schafelner. 2025-02-28. A parallel-in-time solver for nonlinear degenerate time-periodic parabolic problems. https://arxiv.org/abs/2502.21013

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