{"title":"求解高阶helmholtz型偏微分方程的改进虚点边界结法","authors":"L. Liu, L.L. Zhang, M. Lei, R.P. Niu","doi":"10.1016/j.camwa.2025.04.017","DOIUrl":null,"url":null,"abstract":"<div><div>An improved boundary knot method (IBKM) is proposed to enhance the performance of BKM in solving homogeneous high-order Helmholtz-type partial differential equations. Compared with the classical BKM where the sources are always placed on the physical boundary as collocation points, the new sources named fictitious points are now placed on multi-layer extended pseudo boundaries. This modification leads to higher accuracy without the loss of efficiency. Numerical examples are presented to demonstrate the superiority of the IBKM.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 36-47"},"PeriodicalIF":2.5000,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The improved boundary knot method with fictitious points for solving high-order Helmholtz-type PDEs\",\"authors\":\"L. Liu, L.L. Zhang, M. Lei, R.P. Niu\",\"doi\":\"10.1016/j.camwa.2025.04.017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>An improved boundary knot method (IBKM) is proposed to enhance the performance of BKM in solving homogeneous high-order Helmholtz-type partial differential equations. Compared with the classical BKM where the sources are always placed on the physical boundary as collocation points, the new sources named fictitious points are now placed on multi-layer extended pseudo boundaries. This modification leads to higher accuracy without the loss of efficiency. Numerical examples are presented to demonstrate the superiority of the IBKM.</div></div>\",\"PeriodicalId\":55218,\"journal\":{\"name\":\"Computers & Mathematics with Applications\",\"volume\":\"191 \",\"pages\":\"Pages 36-47\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2025-08-01\",\"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/S0898122125001622\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/4/25 0:00:00\",\"PubModel\":\"Epub\",\"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/S0898122125001622","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/25 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The improved boundary knot method with fictitious points for solving high-order Helmholtz-type PDEs
An improved boundary knot method (IBKM) is proposed to enhance the performance of BKM in solving homogeneous high-order Helmholtz-type partial differential equations. Compared with the classical BKM where the sources are always placed on the physical boundary as collocation points, the new sources named fictitious points are now placed on multi-layer extended pseudo boundaries. This modification leads to higher accuracy without the loss of efficiency. Numerical examples are presented to demonstrate the superiority of the IBKM.
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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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