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

We present a new multigrid scheme for solving the Poisson equation withDirichlet boundary conditions on a Cartesian grid with irregular domainboundaries. This scheme was developed in the context of the Adaptive MeshRefinement (AMR) schemes based on a graded-octree data structure. The Poissonequation is solved on a level-by-level basis, using a "one-way interface"scheme in which boundary conditions are interpolated from the previous coarserlevel solution. Such a scheme is particularly well suited for self-gravitatingastrophysical flows requiring an adaptive time stepping strategy. Byconstructing a multigrid hierarchy covering the active cells of each AMR level,we have designed a memory-efficient algorithm that can benefit fully from themultigrid acceleration. We present a simple method for capturing the boundaryconditions across the multigrid hierarchy, based on a second-order accuratereconstruction of the boundaries of the multigrid levels. In case of verycomplex boundaries, small scale features become smaller than the discretizationcell size of coarse multigrid levels and convergence problems arise. We proposea simple solution to address these issues. Using our scheme, the convergencerate usually depends on the grid size for complex grids, but good linearconvergence is maintained. The proposed method was successfully implemented ondistributed memory architectures in the RAMSES code, for which we present anddiscuss convergence and accuracy properties as well as timing performances.

A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries