{"id":21419523,"url":"https://github.com/rezrazi/fem-1d","last_synced_at":"2025-03-16T19:41:17.398Z","repository":{"id":169808961,"uuid":"116143405","full_name":"Rezrazi/FEM-1D","owner":"Rezrazi","description":"Application pour évaluer la solution d'une équation différentielle avec la MEF en 1D","archived":false,"fork":false,"pushed_at":"2019-03-26T18:11:09.000Z","size":2261,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-01-23T06:14:40.766Z","etag":null,"topics":["differential-equations","finite-element-methods","matlab","matlab-application","matlab-gui"],"latest_commit_sha":null,"homepage":null,"language":"MATLAB","has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/Rezrazi.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2018-01-03T14:02:41.000Z","updated_at":"2020-12-08T08:32:20.000Z","dependencies_parsed_at":null,"dependency_job_id":"e3b38c05-3cc0-48af-b829-f643741c35b7","html_url":"https://github.com/Rezrazi/FEM-1D","commit_stats":null,"previous_names":["rezrazi/fem-1d"],"tags_count":1,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Rezrazi%2FFEM-1D","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Rezrazi%2FFEM-1D/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Rezrazi%2FFEM-1D/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Rezrazi%2FFEM-1D/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/Rezrazi","download_url":"https://codeload.github.com/Rezrazi/FEM-1D/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":243922208,"owners_count":20369370,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["differential-equations","finite-element-methods","matlab","matlab-application","matlab-gui"],"created_at":"2024-11-22T19:42:03.661Z","updated_at":"2025-03-16T19:41:17.369Z","avatar_url":"https://github.com/Rezrazi.png","language":"MATLAB","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Méthode d'éléments finis en 1D\n![GitHub](https://img.shields.io/github/license/rezrazi/FEM-1D.svg?style=plastic)\n![GitHub release](https://img.shields.io/github/release/rezrazi/MEF-1D.svg)  \n\n![Splash](https://i.imgur.com/npm5Cny.png)\n\nConsidérant l'équation différentielle suivante : \n$$\\alpha\\ddot{u}+\\beta u = f$$\nOn cherche à évaluer la solution de cette équation numériquement à l'aide d'un script écrit sous Matlab.\n\n## Téléchargements\nhttps://github.com/Rezrazi/FEM-1D/releases\n## Concept\nLe programme **MEFSolution** fonctionne de la manière suivante : \n1. Maillage du domaine.\n2. Calcul des matrices élémentaires avec la méthode de Boole.\n3. Assemblage des matrices élémentaires en matrice globale pour tout le domaine.\n4. Résolution numérique du problème.\n5. Evaluation de l'erreur éventuelle.\n\nLe programme prend donc les paramètres suivants :\n- Le domaine en 1D [a,b]\n- Pas de maillage\n- Coefficients alpha et beta\n- Fonction 2ème membre\n\n## Utilisation\n![Interface](https://i.imgur.com/Hq44K8A.png)\n*L'interface générale de l'application*\n\nSaisie des données d'entrée\n![Données entrée](https://i.imgur.com/yibPcvP.png)\n\nSi on désire évaluer l'erreur au cas ou la solution exacte du problème est connue\n![Analyse d'erreur](https://i.imgur.com/D2V2ZpS.png)\n\nChoisir la méthode d'approximation (P1/P2) et si le programme doit exporter\n![Méthode et exportation](https://i.imgur.com/rn1QXOE.png)\n\nAprès saisie, lancer l'évaluation, un timer enregistre le temps de fonctionnement de l'application  \n![Evaluation](https://i.imgur.com/szOrquw.png)\n\nPanel des résultats, regroupe les éléments suivants : \n- Maillage\n- Solution évaluée\n- Comparaison des solution (En cas d'analyse d'erreur)\n- Analyse d'erreur\n- Erreur relative\n- Log, suivi des étapes effectuées  \n\n\n![Résultats](https://i.imgur.com/KmxzTRG.png)\n\n## Exemple d'évaluation\nPrenons le cas où $$f(x) = sin(x)$$ et $$\\alpha=1$$ et $$\\beta=2$$\n### Maillage\n![](https://i.imgur.com/n4FjqoN.png)\n### Solution évaluée\n![](https://i.imgur.com/6HIB9lI.png)\n### Comparaison de solutions\n![](https://i.imgur.com/2ESO77s.png)\n### Analyse d'erreur\n![](https://i.imgur.com/2ESO77s.png)\n### Erreur relative\n![](https://i.imgur.com/lQQprmR.png)\n### Log\n![](https://i.imgur.com/Ck6M8wo.png)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frezrazi%2Ffem-1d","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Frezrazi%2Ffem-1d","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frezrazi%2Ffem-1d/lists"}