Additive domain decomposition operator splittings – convergence analyses in a dissipative framework

Eskil Hansen, Erik Henningsson

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Sammanfattning

We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a parabolic system can then be interpreted as an operator splitting scheme applied to an abstract evolution equation governed by a maximal dissipative vector field. By utilizing this abstract setting, we derive an optimal temporal error analysis for the two most common choices of domain decomposition based integrators. Namely, alternating direction implicit schemes and additive splitting schemes of first and second order. For the standard first-order additive splitting scheme we also extend the error analysis to semilinear evolution equations, which may only have mild solutions. The theoretical results are finally illustrated by numerical experiments.
Originalspråkengelska
Sidor (från-till)1496-1519
Antal sidor24
TidskriftIMA Journal of Numerical Analysis
Volym37
Nummer3
Tidigt onlinedatum2016 sep. 15
DOI
StatusPublished - 2017

Ämnesklassifikation (UKÄ)

  • Beräkningsmatematik

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  • Erik Henningsson

    Eskil Hansen (Första/primär/huvudhandledare)

    20112016

    Aktivitet: Examination och handledarskapHandledning av forskarstuderande

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