A Symbolic Transformation Language and its Application to a Multiscale Method
Identifieur interne : 000885 ( Main/Exploration ); précédent : 000884; suivant : 000886A Symbolic Transformation Language and its Application to a Multiscale Method
Auteurs : Walid Belkhir [France] ; Alain Giorgetti [France] ; Michel Lenczner [France]Source :
- Journal of Symbolic Computation [ 0747-7171 ] ; 2014-11-03.
Abstract
The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale methods approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into account a wide range of geometries combining thin and periodic structures with the possibility of multiple nested scales. In this paper we present a transformation language that will make the development of MEMSALab more feasible. It is proposed as a Maple package for rule-based programming, rewriting strategies and their combination with standard Maple code. We illustrate the practical interest of this language by using it to encode two examples of multiscale derivations, namely the two-scale limit of the derivative operator and the two-scale model of the stationary heat equation.
Url:
Affiliations:
- France
- Franche-Comté, Grand Est, Lorraine (région)
- Belfort, Besançon, Metz, Nancy
- Université de Bourgogne Franche-Comté, Université de Franche-Comté, Université de Lorraine, Université de technologie de Belfort-Montbéliard
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Le document en format XML
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Sciences et Technologies</orgName><orgName type="acronym">FEMTO-ST</orgName><desc><address><addrLine>32 avenue de l'Observatoire 25044 BESANCON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://www.femto-st.fr</ref></desc><listRelation><relation active="#struct-242365" type="direct"></relation><relation active="#struct-300261" type="direct"></relation><relation active="#struct-300360" type="direct"></relation><relation name="UMR6174" active="#struct-441569" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-242365" type="direct"><org type="institution" xml:id="struct-242365" status="VALID"><idno type="IdRef">026403188</idno><idno type="ISNI">0000 0001 2188 3779 </idno><orgName>Université de Franche-Comté</orgName><orgName type="acronym">UFC</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.univ-fcomte.fr</ref></desc></org></tutelle><tutelle active="#struct-300261" type="direct"><org type="institution" xml:id="struct-300261" status="VALID"><orgName>Université de Technologie de Belfort-Montbeliard</orgName><orgName type="acronym">UTBM</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300360" type="direct"><org type="institution" xml:id="struct-300360" status="VALID"><orgName>Ecole Nationale Supérieure de Mécanique et des Microtechniques</orgName><orgName type="acronym">ENSMM</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle name="UMR6174" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city" wicri:auto="siege">Besançon</settlement><region type="region" nuts="2">Franche-Comté</region></placeName><orgName type="university">Université de Franche-Comté</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName><placeName><settlement type="city" wicri:auto="siege">Belfort</settlement><region type="region" nuts="2">Franche-Comté</region></placeName><orgName type="university">Université de technologie de Belfort-Montbéliard</orgName></affiliation></author></analytic><series><title level="j">Journal of Symbolic Computation</title><idno type="ISSN">0747-7171</idno><imprint><date type="datePub">2014-11-03</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale methods approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into account a wide range of geometries combining thin and periodic structures with the possibility of multiple nested scales. In this paper we present a transformation language that will make the development of MEMSALab more feasible. It is proposed as a Maple package for rule-based programming, rewriting strategies and their combination with standard Maple code. We illustrate the practical interest of this language by using it to encode two examples of multiscale derivations, namely the two-scale limit of the derivative operator and the two-scale model of the stationary heat equation.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Franche-Comté</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Belfort</li><li>Besançon</li><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Bourgogne Franche-Comté</li><li>Université de Franche-Comté</li><li>Université de Lorraine</li><li>Université de technologie de Belfort-Montbéliard</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Belkhir, Walid" sort="Belkhir, Walid" uniqKey="Belkhir W" first="Walid" last="Belkhir">Walid Belkhir</name></region><name sortKey="Giorgetti, Alain" sort="Giorgetti, Alain" uniqKey="Giorgetti A" first="Alain" last="Giorgetti">Alain Giorgetti</name><name sortKey="Lenczner, Michel" sort="Lenczner, Michel" uniqKey="Lenczner M" first="Michel" last="Lenczner">Michel Lenczner</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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