{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:22:11Z","timestamp":1777645331262,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T00:00:00Z","timestamp":1443657600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2015,10]]},"abstract":"<jats:p>In this paper we present several graph transformation systems modeling three dimensional h-adaptive Finite Element Method (3D h-FEM) algorithms with tetrahedral finite elements. In our approach a computational mesh is represented by a composite graph and mesh operations are expressed by the graph transformation rules. Each graph transformation system is responsible for different kind of operations. In particular, there is a graph transformation system expressing generation of an initial mesh, generating element matrices and elimination trees for interfacing with direct solver algorithm, a graph transformation system deciding which elements have to be further refined, as well as a graph transformation system responsible for execution of mesh refinements. These graph transformation systems are tested using a graph transformation tool (called GRAGRA), which provides a graphical environment for defining graphs, graph transformation rules and graph transformation systems. In this paper we illustrate the concepts by using an exemplary derivation for a three dimensional projection problem, based on a set of graph transformation rules.<\/jats:p>","DOI":"10.3233\/fi-2015-1248","type":"journal-article","created":{"date-parts":[[2015,9,2]],"date-time":"2015-09-02T17:42:42Z","timestamp":1441215762000},"page":"129-172","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Graph Transformation Systems for Modeling Three Dimensional Finite Element Method. Part I"],"prefix":"10.1177","volume":"140","author":[{"given":"Iwona","family":"Ryszka","sequence":"first","affiliation":[{"name":"Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059, Krak\u00f3w, Poland"}]},{"given":"Anna","family":"Paszy\u0144ska","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059, Krak\u00f3w, Poland"}]},{"given":"Ewa","family":"Grabska","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Reymonta 4, 30-059, Krak\u00f3w, Poland"}]},{"given":"Marcin","family":"Sieniek","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Computer Science, Electronics and Telecommunications, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Krak\u00f3w, Poland."}]},{"given":"Maciej","family":"Paszy\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Computer Science, Electronics and Telecommunications, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Krak\u00f3w, Poland."}]}],"member":"179","published-online":{"date-parts":[[2015,10,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1248","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1248","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:58Z","timestamp":1777444318000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2015-1248"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["10.3233\/FI-2015-1248"],"URL":"https:\/\/doi.org\/10.3233\/fi-2015-1248","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10]]}}}