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Create jocs.md #20

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Create jocs.md
jpfairbanks Jun 13, 2024
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Add link to decapodes paper
jpfairbanks Jun 13, 2024
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20 changes: 20 additions & 0 deletions publications/jocs.md
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---
title: "Decapodes: A diagrammatic tool for representing, composing, and computing spatialized partial differential equations"
image: https://ars.els-cdn.com/content/image/1-s2.0-S1877750324001388-gr1_lrg.jpg
about:
template: solana
---

## Abstract

We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations, a method for composing systems of partial differential equations using an operad of wiring diagrams, and an algorithm for deriving solvers using hypergraphs and string diagrams. The string diagrams are in turn compiled into executable programs using the techniques of categorical data migration, graph traversal, and the discrete exterior calculus. The generated solvers produce numerical solutions consistent with state-of-the-art open source tools as demonstrated by benchmark comparisons with SU2. These numerical experiments demonstrate the feasibility of this approach to multiphysics simulation and identify areas requiring further development.

## Keywords

Multiphysics, Discrete exterior calculus, Numerical methods, Operad algebras

## Links

- [Journal](https://www.sciencedirect.com/science/article/pii/S1877750324001388)
- [Code](https://github.com/AlgebraicJulia/Decapodes.jl)
- [Docs](https://algebraicjulia.github.io/Decapodes.jl/dev/)
4 changes: 4 additions & 0 deletions research.qmd
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---

## Software

### [Decapodes.jl](https://algebraicjulia.github.io/Decapodes.jl/stable/)

Decapodes are a graphical tool for the composition of physical systems.
Ultimately, this library will include tooling which takes advantage of the formalization of physical theories described by DEC provided by CombinatorialSpaces.jl.

Links:

- [Journal of Computational Science](publications/jocs.md)

### [AlgebraicControl.jl](https://github.com/AlgebraicJulia/AlgebraicControl.jl.git)

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