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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We construct a pseudospectral method for the solution of time-dependent,non-linear partial differential equations on a three-dimensional sphericalshell. The problem we address is the treatment of tensor fields on the sphere.As a test case we consider the evolution of a single black hole in numericalgeneral relativity. A natural strategy would be the expansion in tensorspherical harmonics in spherical coordinates. Instead, we consider the simplerand potentially more efficient possibility of a double Fourier expansion on thesphere for tensors in Cartesian coordinates. As usual for the double Fouriermethod, we employ a filter to address time-step limitations and certainstability issues. We find that a tensor filter based on spin-weighted sphericalharmonics is successful, while two simplified, non-spin-weighted filters do notlead to stable evolutions. The derivatives and the filter are implemented bymatrix multiplication for efficiency. A key technical point is the constructionof a matrix multiplication method for the spin-weighted spherical harmonicfilter. As example for the efficient parallelization of the double Fourier,spin-weighted filter method we discuss an implementation on a GPU, whichachieves a speed-up of up to a factor of 20 compared to a single core CPUimplementation.

A pseudospectral matrix method for time-dependent tensor fields on a spherical shell