Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM
Purpose The purpose of this paper is to develop a mesh-free algorithm based on the least square support vector machines method for numerical simulation of the modified Helmholtz equations. Design/methodology/approach The proposed method deals with a Cauchy problem for the modified Helmholtz equation...
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| Veröffentlicht in: | Engineering computations 2021-02, Vol.38 (2), p.1024-1036 |
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| container_title | Engineering computations |
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| creator | Wu, Ziku Han, Xiaoming Li, GuoFeng |
| description | Purpose
The purpose of this paper is to develop a mesh-free algorithm based on the least square support vector machines method for numerical simulation of the modified Helmholtz equations.
Design/methodology/approach
The proposed method deals with a Cauchy problem for the modified Helmholtz equations. The algorithm converts the problem into a quadratic programming. It can be divided into three steps. First, some training points are allocated. Then, an approximate function is constructed. Finally, the shape parameters are estimated.
Findings
The proposed method's stability is discussed. Numerical experiments are conducted to check the efficiency of the algorithm. The proposed method is found to feasible for the ill-posed problems of the modified Helmholtz equations.
Originality/value
The originality lies in that the proposed method is applied to solve the modified Helmholtz equations for the first time, and the expected results are obtained. |
| doi_str_mv | 10.1108/EC-04-2019-0168 |
| format | Article |
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The purpose of this paper is to develop a mesh-free algorithm based on the least square support vector machines method for numerical simulation of the modified Helmholtz equations.
Design/methodology/approach
The proposed method deals with a Cauchy problem for the modified Helmholtz equations. The algorithm converts the problem into a quadratic programming. It can be divided into three steps. First, some training points are allocated. Then, an approximate function is constructed. Finally, the shape parameters are estimated.
Findings
The proposed method's stability is discussed. Numerical experiments are conducted to check the efficiency of the algorithm. The proposed method is found to feasible for the ill-posed problems of the modified Helmholtz equations.
Originality/value
The originality lies in that the proposed method is applied to solve the modified Helmholtz equations for the first time, and the expected results are obtained.</description><identifier>ISSN: 0264-4401</identifier><identifier>EISSN: 1758-7077</identifier><identifier>DOI: 10.1108/EC-04-2019-0168</identifier><language>eng</language><publisher>Bradford: Emerald Publishing Limited</publisher><subject>Algorithms ; Cauchy problems ; Design modifications ; Finite element method ; Helmholtz equations ; Ill posed problems ; Meshless methods ; Numerical analysis ; Parameter estimation ; Quadratic programming ; Regularization methods ; Support vector machines</subject><ispartof>Engineering computations, 2021-02, Vol.38 (2), p.1024-1036</ispartof><rights>Emerald Publishing Limited</rights><rights>Emerald Publishing Limited 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c262t-4cacd4cb8216d3440b0c796dbe46354123ead7edad300acf239df4aad1b36f423</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.emerald.com/insight/content/doi/10.1108/EC-04-2019-0168/full/html$$EHTML$$P50$$Gemerald$$H</linktohtml><link.rule.ids>314,780,784,966,11634,27923,27924,52688</link.rule.ids></links><search><creatorcontrib>Wu, Ziku</creatorcontrib><creatorcontrib>Han, Xiaoming</creatorcontrib><creatorcontrib>Li, GuoFeng</creatorcontrib><title>Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM</title><title>Engineering computations</title><description>Purpose
The purpose of this paper is to develop a mesh-free algorithm based on the least square support vector machines method for numerical simulation of the modified Helmholtz equations.
Design/methodology/approach
The proposed method deals with a Cauchy problem for the modified Helmholtz equations. The algorithm converts the problem into a quadratic programming. It can be divided into three steps. First, some training points are allocated. Then, an approximate function is constructed. Finally, the shape parameters are estimated.
Findings
The proposed method's stability is discussed. Numerical experiments are conducted to check the efficiency of the algorithm. The proposed method is found to feasible for the ill-posed problems of the modified Helmholtz equations.
Originality/value
The originality lies in that the proposed method is applied to solve the modified Helmholtz equations for the first time, and the expected results are obtained.</description><subject>Algorithms</subject><subject>Cauchy problems</subject><subject>Design modifications</subject><subject>Finite element method</subject><subject>Helmholtz equations</subject><subject>Ill posed problems</subject><subject>Meshless methods</subject><subject>Numerical analysis</subject><subject>Parameter estimation</subject><subject>Quadratic programming</subject><subject>Regularization methods</subject><subject>Support vector machines</subject><issn>0264-4401</issn><issn>1758-7077</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNptkD1PwzAURS0EEqUws1piNn3-aJyMKCoUKYihgNgsx3ZoqqRu7WQov55EYUFiess9910dhG4p3FMK6WKVExCEAc0I0CQ9QzMqlymRIOU5mgFLBBEC6CW6inEHAJJzmKHPwumwr_dfOPqm72q_j7jzWONc92Z7wofgy8a1uPIBd1uHW2_rqnYWr13Tbn3TfWN37PUE9nEsKjZk8_FyjS4q3UR383vn6P1x9ZavSfH69Jw_FMSwhHVEGG2sMGXKaGL5MLAEI7PElk4kfCko405b6ay2HECbivHMVkJrS0ueVILxObqbeoelx97FTu18H_bDS8VEKiHNllkypBZTygQfY3CVOoS61eGkKKhRn1rlCoQa9alR30DcT4RrXdCN_Qf445v_AJxCcHw</recordid><startdate>20210208</startdate><enddate>20210208</enddate><creator>Wu, Ziku</creator><creator>Han, Xiaoming</creator><creator>Li, GuoFeng</creator><general>Emerald Publishing Limited</general><general>Emerald Group Publishing Limited</general><scope>AAYXX</scope><scope>CITATION</scope><scope>0U~</scope><scope>1-H</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L.0</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20210208</creationdate><title>Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM</title><author>Wu, Ziku ; Han, Xiaoming ; Li, GuoFeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c262t-4cacd4cb8216d3440b0c796dbe46354123ead7edad300acf239df4aad1b36f423</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>Cauchy problems</topic><topic>Design modifications</topic><topic>Finite element method</topic><topic>Helmholtz equations</topic><topic>Ill posed problems</topic><topic>Meshless methods</topic><topic>Numerical analysis</topic><topic>Parameter estimation</topic><topic>Quadratic programming</topic><topic>Regularization methods</topic><topic>Support vector machines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Ziku</creatorcontrib><creatorcontrib>Han, Xiaoming</creatorcontrib><creatorcontrib>Li, GuoFeng</creatorcontrib><collection>CrossRef</collection><collection>Global News & ABI/Inform Professional</collection><collection>Trade PRO</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Professional Standard</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Engineering computations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wu, Ziku</au><au>Han, Xiaoming</au><au>Li, GuoFeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM</atitle><jtitle>Engineering computations</jtitle><date>2021-02-08</date><risdate>2021</risdate><volume>38</volume><issue>2</issue><spage>1024</spage><epage>1036</epage><pages>1024-1036</pages><issn>0264-4401</issn><eissn>1758-7077</eissn><abstract>Purpose
The purpose of this paper is to develop a mesh-free algorithm based on the least square support vector machines method for numerical simulation of the modified Helmholtz equations.
Design/methodology/approach
The proposed method deals with a Cauchy problem for the modified Helmholtz equations. The algorithm converts the problem into a quadratic programming. It can be divided into three steps. First, some training points are allocated. Then, an approximate function is constructed. Finally, the shape parameters are estimated.
Findings
The proposed method's stability is discussed. Numerical experiments are conducted to check the efficiency of the algorithm. The proposed method is found to feasible for the ill-posed problems of the modified Helmholtz equations.
Originality/value
The originality lies in that the proposed method is applied to solve the modified Helmholtz equations for the first time, and the expected results are obtained.</abstract><cop>Bradford</cop><pub>Emerald Publishing Limited</pub><doi>10.1108/EC-04-2019-0168</doi><tpages>13</tpages></addata></record> |
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| ispartof | Engineering computations, 2021-02, Vol.38 (2), p.1024-1036 |
| issn | 0264-4401 1758-7077 |
| language | eng |
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| source | Emerald Journals |
| subjects | Algorithms Cauchy problems Design modifications Finite element method Helmholtz equations Ill posed problems Meshless methods Numerical analysis Parameter estimation Quadratic programming Regularization methods Support vector machines |
| title | Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM |
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