{"title":"原始混合有限元的MATLAB矢量化实现","authors":"Harish Nagula Mallesham , Kamana Porwal , Jan Valdman , Sanjib Kumar Acharya","doi":"10.1016/j.camwa.2024.12.017","DOIUrl":null,"url":null,"abstract":"<div><div>We present efficient MATLAB implementations of the lowest-order primal hybrid finite element method (FEM) for linear second-order elliptic and parabolic problems with mixed boundary conditions in two spatial dimensions. We employ backward Euler and the Crank-Nicolson finite difference scheme for the complete discrete setup of the parabolic problem. All the codes presented are fully vectorized using matrix-wise array operations. Numerical experiments are conducted to show the performance of the software.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"180 ","pages":"Pages 144-165"},"PeriodicalIF":2.9000,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Vectorized implementation of primal hybrid FEM in MATLAB\",\"authors\":\"Harish Nagula Mallesham , Kamana Porwal , Jan Valdman , Sanjib Kumar Acharya\",\"doi\":\"10.1016/j.camwa.2024.12.017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We present efficient MATLAB implementations of the lowest-order primal hybrid finite element method (FEM) for linear second-order elliptic and parabolic problems with mixed boundary conditions in two spatial dimensions. We employ backward Euler and the Crank-Nicolson finite difference scheme for the complete discrete setup of the parabolic problem. All the codes presented are fully vectorized using matrix-wise array operations. Numerical experiments are conducted to show the performance of the software.</div></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":\"180 \",\"pages\":\"Pages 144-165\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Mathematics with Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0898122124005625\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0898122124005625","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Vectorized implementation of primal hybrid FEM in MATLAB
We present efficient MATLAB implementations of the lowest-order primal hybrid finite element method (FEM) for linear second-order elliptic and parabolic problems with mixed boundary conditions in two spatial dimensions. We employ backward Euler and the Crank-Nicolson finite difference scheme for the complete discrete setup of the parabolic problem. All the codes presented are fully vectorized using matrix-wise array operations. Numerical experiments are conducted to show the performance of the software.
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Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).
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