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/

Zendy Plus

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

Zendy Tools

Zendy Open

For time-dependent problems with high-contrast multiscale coefficients, thetime step size for explicit methods is affected by the magnitude of thecoefficient parameter. With a suitable construction of multiscale space, onecan achieve a stable temporal splitting scheme where the time step size isindependent of the contrast. Consider the parabolic equation with heterogeneousdiffusion parameter, the flow rates vary significantly in different regions dueto the high-contrast features of the diffusivity. In this work, we aim tointroduce a multirate partially explicit splitting scheme to achieve efficientsimulation with the desired accuracy. We first design multiscale subspaces tohandle flow with different speed. For the fast flow, we obtain alow-dimensional subspace with respect to the high-diffusive component and adoptan implicit time discretization scheme. The other multiscale subspace will takecare of the slow flow, and the corresponding degrees of freedom are treatedexplicitly. Then a multirate time stepping is introduced for the two parts. Thestability of the multirate methods is analyzed for the partially explicitscheme. Moreover, we derive local error estimators corresponding to the twocomponents of the solutions and provide an upper bound of the errors. Anadaptive local temporal refinement framework is then proposed to achieve highercomputational efficiency. Several numerical tests are presented to demonstratethe performance of the proposed method.

Multirate partially explicit scheme for multiscale flow problems