From 73717b45931bf61711e4fb6efb3ea8414821b44d Mon Sep 17 00:00:00 2001 From: James Date: Thu, 13 Jun 2024 12:26:39 -0400 Subject: [PATCH 1/2] Create jocs.md --- research/jocs.md | 20 ++++++++++++++++++++ 1 file changed, 20 insertions(+) create mode 100644 research/jocs.md diff --git a/research/jocs.md b/research/jocs.md new file mode 100644 index 0000000..6ce075c --- /dev/null +++ b/research/jocs.md @@ -0,0 +1,20 @@ +--- +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/) From f24165740cbd8a418736e4cd17eea29ced9f4658 Mon Sep 17 00:00:00 2001 From: "James P. Fairbanks" Date: Thu, 13 Jun 2024 12:36:23 -0400 Subject: [PATCH 2/2] Add link to decapodes paper --- {research => publications}/jocs.md | 0 research.qmd | 4 ++++ 2 files changed, 4 insertions(+) rename {research => publications}/jocs.md (100%) diff --git a/research/jocs.md b/publications/jocs.md similarity index 100% rename from research/jocs.md rename to publications/jocs.md diff --git a/research.qmd b/research.qmd index 7b2cb77..3cc58ed 100644 --- a/research.qmd +++ b/research.qmd @@ -3,11 +3,15 @@ title: "Research" --- ## 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)