English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Parallel-in-time algorithms have been successfully employed for reducingtime-to-solution of a variety of partial differential equations, especially fordiffusive (parabolic-type) equations. A major failing of parallel-in-timeapproaches to date, however, is that most methods show instabilities or poorconvergence for hyperbolic problems. This paper focuses on the analysis of theconvergence behavior of multigrid methods for the parallel-in-time solution ofhyperbolic problems. Three analysis tools are considered that differ, inparticular, in the treatment of the time dimension: (1) space-time localFourier analysis, using a Fourier ansatz in space and time, (2) semi-algebraicmode analysis, coupling standard local Fourier analysis approaches in spacewith algebraic computation in time, and (3) a two-level reduction analysis,considering error propagation only on the coarse time grid. In this paper, weshow how insights from reduction analysis can be used to improve feasibility ofthe semi-algebraic mode analysis, resulting in a tool that offers the bestfeatures of both analysis techniques. Following validating numerical results,we investigate what insights the combined analysis framework can offer for twomodel hyperbolic problems, the linear advection equation in one space dimensionand linear elasticity in two space dimensions.

Convergence analysis for parallel-in-time solution of hyperbolic systems