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

A common numerical task is to represent functions which are highly spatiallyanisotropic, and to solve differential equations related to these functions.One way such anisotropy arises is that information transfer along one spatialdirection is much faster than in others. In this situation, the derivative ofthe function is small in the local direction of a vector field $\mathbf{b}$. Inorder to define a discrete representation, a set of surfaces $M_i$ indexed byan integer $i$ are chosen such that mapping along the field $\mathbf{b}$induces a one-to-one relation between the points on surface $M_i$ to those on$M_{i+1}$. For simple cases $M_i$ may be surfaces of constant coordinate value.On each surface $M_i$, a function description is constructed using basisfunctions defined on a regular structured mesh. The definition of each basisfunction is extended from the surface $M$ along the lines of the field$\mathbf{b}$ by multiplying it by a smooth compact support function whoseargument increases with distance along $\mathbf{b}$. Function values areevaluated by summing contributions associated with each surface $M_i$. Thisdoes not require any special connectivity of the meshes used in theneighbouring surfaces $M$, which substantially simplifies the meshing problemcompared to attempting to find a space filling anisotropic mesh. We explore thenumerical properties of the scheme, and show that it can be used to efficientlysolve differential equations for certain anisotropic problems.

A partially mesh-free scheme for representing anisotropic spatial variations along field lines