{"title":"基于节点的一致不符梯度平滑方案,用于高效伽勒金无网格计算","authors":"Liheng Fan, Like Deng, Dongdong Wang","doi":"10.1007/s00366-024-02027-6","DOIUrl":null,"url":null,"abstract":"<p>The stabilized conforming nodal integration (SCNI) is currently widely employed in Galerkin meshfree formulation. A key ingredient of SCNI is the strain or gradient smoothing defined within a set of conforming nodal representative domains, which usually are formed by the auxiliary points in addition to the meshfree nodes. Nonetheless, these auxiliary points may significantly increase the storage requirement and computational cost of SCNI, in comparison with the direct nodal integration. In order to address this issue, a purely node-based consistent non-conforming gradient smoothing (CNGS) scheme is proposed herein to accelerate the Galerkin meshfree computation. In the proposed method, only the meshfree nodes are employed to construct overlapping and non-conforming nodal representative domains, which are then adopted for the nodal gradient smoothing operation. However, unlike the existing non-conforming gradient smoothing algorithms that commonly violate the integration consistency, the proposed method maintains the desirable integration consistency through a proportional separation between the nodal gradient smoothing domains and the nodal integration domains, which essentially ensures the meshfree solution accuracy. Meanwhile, due to the absence of auxiliary points in the gradient smoothing evaluation, the computational efficiency is substantially improved by the proposed method of CNGS compared with SCNI. The effectiveness of the proposed methodology is well demonstrated by numerical results.</p>","PeriodicalId":11696,"journal":{"name":"Engineering with Computers","volume":null,"pages":null},"PeriodicalIF":8.7000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A node-based consistent non-conforming gradient smoothing scheme for highly efficient Galerkin meshfree formulation\",\"authors\":\"Liheng Fan, Like Deng, Dongdong Wang\",\"doi\":\"10.1007/s00366-024-02027-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The stabilized conforming nodal integration (SCNI) is currently widely employed in Galerkin meshfree formulation. A key ingredient of SCNI is the strain or gradient smoothing defined within a set of conforming nodal representative domains, which usually are formed by the auxiliary points in addition to the meshfree nodes. Nonetheless, these auxiliary points may significantly increase the storage requirement and computational cost of SCNI, in comparison with the direct nodal integration. In order to address this issue, a purely node-based consistent non-conforming gradient smoothing (CNGS) scheme is proposed herein to accelerate the Galerkin meshfree computation. In the proposed method, only the meshfree nodes are employed to construct overlapping and non-conforming nodal representative domains, which are then adopted for the nodal gradient smoothing operation. However, unlike the existing non-conforming gradient smoothing algorithms that commonly violate the integration consistency, the proposed method maintains the desirable integration consistency through a proportional separation between the nodal gradient smoothing domains and the nodal integration domains, which essentially ensures the meshfree solution accuracy. Meanwhile, due to the absence of auxiliary points in the gradient smoothing evaluation, the computational efficiency is substantially improved by the proposed method of CNGS compared with SCNI. The effectiveness of the proposed methodology is well demonstrated by numerical results.</p>\",\"PeriodicalId\":11696,\"journal\":{\"name\":\"Engineering with Computers\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.7000,\"publicationDate\":\"2024-08-17\",\"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/s00366-024-02027-6\",\"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/s00366-024-02027-6","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 node-based consistent non-conforming gradient smoothing scheme for highly efficient Galerkin meshfree formulation
The stabilized conforming nodal integration (SCNI) is currently widely employed in Galerkin meshfree formulation. A key ingredient of SCNI is the strain or gradient smoothing defined within a set of conforming nodal representative domains, which usually are formed by the auxiliary points in addition to the meshfree nodes. Nonetheless, these auxiliary points may significantly increase the storage requirement and computational cost of SCNI, in comparison with the direct nodal integration. In order to address this issue, a purely node-based consistent non-conforming gradient smoothing (CNGS) scheme is proposed herein to accelerate the Galerkin meshfree computation. In the proposed method, only the meshfree nodes are employed to construct overlapping and non-conforming nodal representative domains, which are then adopted for the nodal gradient smoothing operation. However, unlike the existing non-conforming gradient smoothing algorithms that commonly violate the integration consistency, the proposed method maintains the desirable integration consistency through a proportional separation between the nodal gradient smoothing domains and the nodal integration domains, which essentially ensures the meshfree solution accuracy. Meanwhile, due to the absence of auxiliary points in the gradient smoothing evaluation, the computational efficiency is substantially improved by the proposed method of CNGS compared with SCNI. The effectiveness of the proposed methodology is well demonstrated by numerical results.
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.