{"title":"解决半空间吃传导问题的稳定高效无限无网格方法","authors":"Kuan-Chung Lin, Ting-Wei Chen, Huai-Liang Hsieh","doi":"10.1007/s00366-024-01960-w","DOIUrl":null,"url":null,"abstract":"<p>This study introduces an innovative dynamic infinite meshfree method for robust and efficient solutions to half-space problems. This approach seamlessly couples this method with the nodal integral reproducing kernel particle method to discretize half-spaces defined by an artificial boundary. The infinite meshfree shape function is uniquely constructed using the 1D reproducing kernel shape function combined with the boundary singular kernel method, ensuring the Kronecker delta property on artificial boundaries. Coupled with the wave-transfer function, the proposed approach models dissipation actions effectively. The infinite domain simulation employs the dummy node method, enhanced by Newton–Cotes integrals. To ensure solution stability and convergence, our approach is based on the Galerkin weak form of the domain integral method. To combat the challenges of instability and imprecision, we integrated the stabilized conforming nodal integration method and the naturally stable nodal integration. The proposed methods efficacy is validated through various benchmark problems, with preliminary results showcasing superior precision and stability.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7000,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A stable and efficient infinite meshfree approach for solving half-space eat conduction problems\",\"authors\":\"Kuan-Chung Lin, Ting-Wei Chen, Huai-Liang Hsieh\",\"doi\":\"10.1007/s00366-024-01960-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This study introduces an innovative dynamic infinite meshfree method for robust and efficient solutions to half-space problems. This approach seamlessly couples this method with the nodal integral reproducing kernel particle method to discretize half-spaces defined by an artificial boundary. The infinite meshfree shape function is uniquely constructed using the 1D reproducing kernel shape function combined with the boundary singular kernel method, ensuring the Kronecker delta property on artificial boundaries. Coupled with the wave-transfer function, the proposed approach models dissipation actions effectively. The infinite domain simulation employs the dummy node method, enhanced by Newton–Cotes integrals. To ensure solution stability and convergence, our approach is based on the Galerkin weak form of the domain integral method. To combat the challenges of instability and imprecision, we integrated the stabilized conforming nodal integration method and the naturally stable nodal integration. The proposed methods efficacy is validated through various benchmark problems, with preliminary results showcasing superior precision and stability.</p>\",\"PeriodicalId\":11696,\"journal\":{\"name\":\"Engineering with Computers\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.7000,\"publicationDate\":\"2024-03-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering with Computers\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s00366-024-01960-w\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering with Computers","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s00366-024-01960-w","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
A stable and efficient infinite meshfree approach for solving half-space eat conduction problems
This study introduces an innovative dynamic infinite meshfree method for robust and efficient solutions to half-space problems. This approach seamlessly couples this method with the nodal integral reproducing kernel particle method to discretize half-spaces defined by an artificial boundary. The infinite meshfree shape function is uniquely constructed using the 1D reproducing kernel shape function combined with the boundary singular kernel method, ensuring the Kronecker delta property on artificial boundaries. Coupled with the wave-transfer function, the proposed approach models dissipation actions effectively. The infinite domain simulation employs the dummy node method, enhanced by Newton–Cotes integrals. To ensure solution stability and convergence, our approach is based on the Galerkin weak form of the domain integral method. To combat the challenges of instability and imprecision, we integrated the stabilized conforming nodal integration method and the naturally stable nodal integration. The proposed methods efficacy is validated through various benchmark problems, with preliminary results showcasing superior precision and stability.
期刊介绍:
Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.