Decapodes: A Diagrammatic Tool for Representing, Composing, and Computing Spatialized Partial Differential Equations

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 equat...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Morris, Luke, Baas, Andrew, Arias, Jesus, Gatlin, Maia, Patterson, Evan, Fairbanks, James P
Format: Article
Language:English
Subjects:
Algorithms
Calculus
Partial differential equations
Solvers
Strings
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Morris, Luke
Baas, Andrew
Arias, Jesus
Gatlin, Maia
Patterson, Evan
Fairbanks, James P
description 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.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2920902547</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2920902547</sourcerecordid><originalsourceid>FETCH-proquest_journals_29209025473</originalsourceid><addsrcrecordid>eNqNjMEKgkAYhJcgSMp3WOiasK2a2S3U6BjlXRb9FUX3X3f10tO3Rg_QaWb4ZmZFHO77R-8ccL4hrjEdY4yfIh6GvkOmFEqhsAJzoVeatqLRYhjE1JY0R-xpjZo-QWkwIKdWNgea4KDQfK2Q1TfOC6EvZWeib99Q0YfQi7eHdQ16mdqQjbNtoDQ7sq5Fb8D96Zbsb1me3D2lcZzBTEWHs5YWFTzmLGY8DCL_v9YH4W9MJw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2920902547</pqid></control><display><type>article</type><title>Decapodes: A Diagrammatic Tool for Representing, Composing, and Computing Spatialized Partial Differential Equations</title><source>Publicly Available Content (ProQuest)</source><creator>Morris, Luke ; Baas, Andrew ; Arias, Jesus ; Gatlin, Maia ; Patterson, Evan ; Fairbanks, James P</creator><creatorcontrib>Morris, Luke ; Baas, Andrew ; Arias, Jesus ; Gatlin, Maia ; Patterson, Evan ; Fairbanks, James P</creatorcontrib><description>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.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Calculus ; Partial differential equations ; Solvers ; Strings</subject><ispartof>arXiv.org, 2024-01</ispartof><rights>2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2920902547?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,37012,44590</link.rule.ids></links><search><creatorcontrib>Morris, Luke</creatorcontrib><creatorcontrib>Baas, Andrew</creatorcontrib><creatorcontrib>Arias, Jesus</creatorcontrib><creatorcontrib>Gatlin, Maia</creatorcontrib><creatorcontrib>Patterson, Evan</creatorcontrib><creatorcontrib>Fairbanks, James P</creatorcontrib><title>Decapodes: A Diagrammatic Tool for Representing, Composing, and Computing Spatialized Partial Differential Equations</title><title>arXiv.org</title><description>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.</description><subject>Algorithms</subject><subject>Calculus</subject><subject>Partial differential equations</subject><subject>Solvers</subject><subject>Strings</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNjMEKgkAYhJcgSMp3WOiasK2a2S3U6BjlXRb9FUX3X3f10tO3Rg_QaWb4ZmZFHO77R-8ccL4hrjEdY4yfIh6GvkOmFEqhsAJzoVeatqLRYhjE1JY0R-xpjZo-QWkwIKdWNgea4KDQfK2Q1TfOC6EvZWeib99Q0YfQi7eHdQ16mdqQjbNtoDQ7sq5Fb8D96Zbsb1me3D2lcZzBTEWHs5YWFTzmLGY8DCL_v9YH4W9MJw</recordid><startdate>20240130</startdate><enddate>20240130</enddate><creator>Morris, Luke</creator><creator>Baas, Andrew</creator><creator>Arias, Jesus</creator><creator>Gatlin, Maia</creator><creator>Patterson, Evan</creator><creator>Fairbanks, James P</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240130</creationdate><title>Decapodes: A Diagrammatic Tool for Representing, Composing, and Computing Spatialized Partial Differential Equations</title><author>Morris, Luke ; Baas, Andrew ; Arias, Jesus ; Gatlin, Maia ; Patterson, Evan ; Fairbanks, James P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_29209025473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Calculus</topic><topic>Partial differential equations</topic><topic>Solvers</topic><topic>Strings</topic><toplevel>online_resources</toplevel><creatorcontrib>Morris, Luke</creatorcontrib><creatorcontrib>Baas, Andrew</creatorcontrib><creatorcontrib>Arias, Jesus</creatorcontrib><creatorcontrib>Gatlin, Maia</creatorcontrib><creatorcontrib>Patterson, Evan</creatorcontrib><creatorcontrib>Fairbanks, James P</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Morris, Luke</au><au>Baas, Andrew</au><au>Arias, Jesus</au><au>Gatlin, Maia</au><au>Patterson, Evan</au><au>Fairbanks, James P</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Decapodes: A Diagrammatic Tool for Representing, Composing, and Computing Spatialized Partial Differential Equations</atitle><jtitle>arXiv.org</jtitle><date>2024-01-30</date><risdate>2024</risdate><eissn>2331-8422</eissn><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.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2024-01
issn 2331-8422
language eng
recordid cdi_proquest_journals_2920902547
source Publicly Available Content (ProQuest)
subjects Algorithms
Calculus
Partial differential equations
Solvers
Strings
title Decapodes: A Diagrammatic Tool for Representing, Composing, and Computing Spatialized Partial Differential Equations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T18%3A46%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Decapodes:%20A%20Diagrammatic%20Tool%20for%20Representing,%20Composing,%20and%20Computing%20Spatialized%20Partial%20Differential%20Equations&rft.jtitle=arXiv.org&rft.au=Morris,%20Luke&rft.date=2024-01-30&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2920902547%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_29209025473%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2920902547&rft_id=info:pmid/&rfr_iscdi=true