Two-step MPS-MFS ghost point method for solving partial differential equations
The fictitious boundary surrounding the domain is required in the implementation of the method of fundamental solutions (MFS). A similar approach of taking a portion of the centres of radial basis functions (RBFs) outside the domain in the context of the method of particular solutions (MPS) is propo...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2021-07, Vol.94, p.38-46 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Young, D.L. Lin, Shin-Ruei Chen, Chuin-Shan Chen, C.S. |
| description | The fictitious boundary surrounding the domain is required in the implementation of the method of fundamental solutions (MFS). A similar approach of taking a portion of the centres of radial basis functions (RBFs) outside the domain in the context of the method of particular solutions (MPS) is proposed to further improve the performance of a two-step MPS-MFS method. Since the shape parameter of RBFs is problem dependent, several known procedures on how to determine a good shape parameter are introduced for solving various types of problems. The proposed method is not only highly accurate but also fairly stable due to the use of the particular solutions and fundamental solutions. To demonstrate the effectiveness of the proposed method, five numerical examples in highly complicate and irregular domains, which include second and fourth order elliptic partial differential equations in 2D and 3D, are presented. |
| doi_str_mv | 10.1016/j.camwa.2021.04.001 |
| format | Article |
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A similar approach of taking a portion of the centres of radial basis functions (RBFs) outside the domain in the context of the method of particular solutions (MPS) is proposed to further improve the performance of a two-step MPS-MFS method. Since the shape parameter of RBFs is problem dependent, several known procedures on how to determine a good shape parameter are introduced for solving various types of problems. The proposed method is not only highly accurate but also fairly stable due to the use of the particular solutions and fundamental solutions. 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To demonstrate the effectiveness of the proposed method, five numerical examples in highly complicate and irregular domains, which include second and fourth order elliptic partial differential equations in 2D and 3D, are presented.</description><subject>Domains</subject><subject>Elliptic functions</subject><subject>Fictitious points method</subject><subject>Method of fundamental solutions</subject><subject>Method of particular solutions</subject><subject>Multiquadrics</subject><subject>Parameters</subject><subject>Partial differential equations</subject><subject>Radial basis function</subject><subject>Radial basis functions</subject><subject>Shape parameter</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kM1OAjEURhujiYg-gZsmrmfs30w7CxeGiJqAmoDrptNpoQSmQ1sgvr0DuHb15SbfuTf3AHCPUY4RLh9XuVabg8oJIjhHLEcIX4ABFpxmvCzFJRggUYkME4KvwU2MK4QQowQNwMf84LOYTAenX7NsOp7BxdLHBDvv2gQ3Ji19A60PMPr13rUL2KmQnFrDxllrgmlPg9nuVHK-jbfgyqp1NHd_OQTf45f56C2bfL6-j54nmaYUp4wRJuqyLiwloiB1RYXGrOTKMst5qXVdoaosCObaMCsajhvLsaqbPnqwRnQIHs57u-C3OxOTXPldaPuTkhSMVZhUJelb9NzSwccYjJVdcBsVfiRG8ihOruRJnDyKk4jJXlxPPZ0p0z-wdybIqJ1ptWlcMDrJxrt_-V_QCXdN</recordid><startdate>20210715</startdate><enddate>20210715</enddate><creator>Young, D.L.</creator><creator>Lin, Shin-Ruei</creator><creator>Chen, Chuin-Shan</creator><creator>Chen, C.S.</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-3611-2982</orcidid></search><sort><creationdate>20210715</creationdate><title>Two-step MPS-MFS ghost point method for solving partial differential equations</title><author>Young, D.L. ; Lin, Shin-Ruei ; Chen, Chuin-Shan ; Chen, C.S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-4248b6b5f32852b938c1467af4f776ccb90965217ce4f8d71df71abddf748bb03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Domains</topic><topic>Elliptic functions</topic><topic>Fictitious points method</topic><topic>Method of fundamental solutions</topic><topic>Method of particular solutions</topic><topic>Multiquadrics</topic><topic>Parameters</topic><topic>Partial differential equations</topic><topic>Radial basis function</topic><topic>Radial basis functions</topic><topic>Shape parameter</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Young, D.L.</creatorcontrib><creatorcontrib>Lin, Shin-Ruei</creatorcontrib><creatorcontrib>Chen, Chuin-Shan</creatorcontrib><creatorcontrib>Chen, C.S.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Young, D.L.</au><au>Lin, Shin-Ruei</au><au>Chen, Chuin-Shan</au><au>Chen, C.S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two-step MPS-MFS ghost point method for solving partial differential equations</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2021-07-15</date><risdate>2021</risdate><volume>94</volume><spage>38</spage><epage>46</epage><pages>38-46</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>The fictitious boundary surrounding the domain is required in the implementation of the method of fundamental solutions (MFS). 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| ispartof | Computers & mathematics with applications (1987), 2021-07, Vol.94, p.38-46 |
| issn | 0898-1221 1873-7668 |
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| source | Elsevier ScienceDirect Journals |
| subjects | Domains Elliptic functions Fictitious points method Method of fundamental solutions Method of particular solutions Multiquadrics Parameters Partial differential equations Radial basis function Radial basis functions Shape parameter |
| title | Two-step MPS-MFS ghost point method for solving partial differential equations |
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