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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Fractional vector calculus is the building block of the fractional partialdifferential equations that model non-local or long-range phenomena, e.g.,anomalous diffusion, fractional electromagnetism, and fractionaladvection-dispersion. In this work, we reformulate a type of fractional vectorcalculus that uses Caputo fractional partial derivatives and discretize thisreformulation using discrete exterior calculus on a cubical complex in thestructure-preserving way, meaning that the continuous-level properties$\operatorname{curl}^\alpha \operatorname{grad}^\alpha = \mathbf{0}$ and$\operatorname{div}^\alpha \operatorname{curl}^\alpha = 0$ hold exactly on thediscrete level. We discuss important properties of our fractional discreteexterior derivatives and verify their second-order convergence in the root meansquare error numerically. Our proposed discretization has the potential toprovide accurate and stable numerical solutions to fractional partialdifferential equations and exactly preserve fundamental physics laws on thediscrete level regardless of the mesh size.

Structure-Preserving Discretization of Fractional Vector Calculus using Discrete Exterior Calculus