DOI: 10.1016/j.camwa.2006.04.013. Meshfree explicit local radial basis function collocation method for diffusion problems

Meshfree explicit local radial basis function collocation method for diffusion problems

10.1016/j.camwa.2006.04.013

Crossref journal-article

Elsevier BV

Computers & Mathematics with Applications (78)

Bibliography

Å arler, B., & Vertnik, R. (2006). Meshfree explicit local radial basis function collocation method for diffusion problems. Computers & Mathematics with Applications, 51(8), 1269â1282.

Authors 2

B. Šarler (first)
R. Vertnik (additional)

References 23 Referenced 307

{'key': '10.1016/j.camwa.2006.04.013_bib1', 'series-title': 'The Meshless Method', 'author': 'Atluri', 'year': '2002'} / The Meshless Method by Atluri (2002)
{'key': '10.1016/j.camwa.2006.04.013_bib2', 'series-title': 'Mesh Free Methods', 'author': 'Liu', 'year': '2003'} / Mesh Free Methods by Liu (2003)
{'key': '10.1016/j.camwa.2006.04.013_bib3', 'series-title': 'The Meshless Method for Domain and BIE Discretisations', 'author': 'Atluri', 'year': '2004'} / The Meshless Method for Domain and BIE Discretisations by Atluri (2004)
{'key': '10.1016/j.camwa.2006.04.013_bib4', 'series-title': 'Advanced Numerical Methods in Heat Transfer', 'first-page': '225', 'article-title': 'Chapter 9: “Meshless Methods”', 'author': 'Šarler', 'year': '2004'} / Advanced Numerical Methods in Heat Transfer / Chapter 9: “Meshless Methods” by Šarler (2004)
{'key': '10.1016/j.camwa.2006.04.013_bib5', 'series-title': 'Radial Basis Function: Theory and Implementations', 'author': 'Buhmann', 'year': '2003'} / Radial Basis Function: Theory and Implementations by Buhmann (2003)
10.1016/0898-1221(90)90271-K / Computers Math. Applic. / Multiquadrics—A scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to parabolic, hyperbolic and elliptic partial differential equations by Kansa (1990)
{'key': '10.1016/j.camwa.2006.04.013_bib7', 'series-title': 'Surface Fitting and Multiresolution Methods', 'first-page': '131', 'article-title': 'Solving partial differential equations by collocation with radial basis functions', 'author': 'Fasshauer', 'year': '1997'} / Surface Fitting and Multiresolution Methods / Solving partial differential equations by collocation with radial basis functions by Fasshauer (1997)
10.1016/S0898-1221(01)00305-4 / Computers Math. Applic. / Comparison analysis between unsymmetric and symmetric RBFCMS for the numerical solution of PDEs by Power (2002)
10.1007/978-3-642-56103-0_6 / Lecture Notes in Computational Science and Engineering / New RBF collocation schemes and kernel RBFs with applications by Chen (2002)
{'key': '10.1016/j.camwa.2006.04.013_bib10', 'first-page': '85', 'article-title': 'Indirect RBFN method with thin plate splines for numerical solution of differential equations', 'volume': '4', 'author': 'Mai-Duy', 'year': '2003', 'journal-title': 'Computer Modeling in Engineering & Sciences'} / Computer Modeling in Engineering & Sciences / Indirect RBFN method with thin plate splines for numerical solution of differential equations by Mai-Duy (2003)
{'key': '10.1016/j.camwa.2006.04.013_bib11', 'first-page': '185', 'article-title': 'A radial basis function collocation approach in computational fluid dynamics', 'volume': '7', 'author': 'Sarler', 'year': '2005', 'journal-title': 'Computer Modeling in Engineering & Sciences'} / Computer Modeling in Engineering & Sciences / A radial basis function collocation approach in computational fluid dynamics by Sarler (2005)
10.1016/S0893-6080(00)00095-2 / Neural Networks / Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks by Mai-Duy (2001)
10.1108/09615530410513809 / Int. J. Numer. Methods Heat & Fluid Flow / Radial basis function collocation method solution of natural convection in porous media by Sarler (2004)
{'key': '10.1016/j.camwa.2006.04.013_bib14', 'first-page': '1', 'article-title': 'Solving the Stefan problem by the RBFCM', 'volume': '44', 'author': 'Kovačević', 'year': '2003', 'journal-title': 'Numer. Heat Transfer, Part B: Fundamentals'} / Numer. Heat Transfer, Part B: Fundamentals / Solving the Stefan problem by the RBFCM by Kovačević (2003)
10.1016/S0898-1221(01)00292-9 / Computers Math. Applic. / Multilevel compact radial basis functions based computational scheme for some elliptic problems by Chen (2002)
10.1016/S0955-7997(01)00092-3 / Engineering Analysis with Boundary Elements / Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations by Mai-Duy (2002)
10.1007/s00466-003-0416-5 / Computational Mechanics / Local multiquadric approximation for solving boundary value problems by Lee (2003)
10.1007/s00466-003-0501-9 / Computational Mechanics / On using radial basis functions in a “finite difference” mode with applications to elasticity problems by Tolstykh (2003)
10.1016/S0045-7825(02)00618-7 / Computer Methods in Applied Mechanics and Engineering / Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations by Shu (2003)
{'key': '10.1016/j.camwa.2006.04.013_bib20', 'series-title': 'Benchmark Tests for Thermal Analysis', 'author': 'Cameron', 'year': '1986'} / Benchmark Tests for Thermal Analysis by Cameron (1986)
10.1002/nme.1620231003 / International Journal for Numerical Methods in Engineering / Comparison of finite element techniques for solidification problems by Dalhuijsen (1986)
10.1016/S0955-7997(97)00113-6 / Engineering Analysis with Boundary Elements / Dual reciprocity boundary element method for convectioe-diffusive solid-liquid phase change problems, Part 2: Numerical examples by Sarler (1998)
{'key': '10.1016/j.camwa.2006.04.013_bib23', 'series-title': 'Conduction of Heat in Solids', 'author': 'Carlsaw', 'year': '1995'} / Conduction of Heat in Solids by Carlsaw (1995)

Dates

Type	When
Created	19 years, 1 month ago (July 18, 2006, 7:13 a.m.)
Deposited	6 years, 7 months ago (Jan. 14, 2019, 9:21 p.m.)
Indexed	1 hour ago (Aug. 21, 2025, 2:16 a.m.)
Issued	19 years, 4 months ago (April 1, 2006)
Published	19 years, 4 months ago (April 1, 2006)
Published Print	19 years, 4 months ago (April 1, 2006)

Funders 0

None

BibTeX

@article{_arler_2006, title={Meshfree explicit local radial basis function collocation method for diffusion problems}, volume={51}, ISSN={0898-1221}, url={http://dx.doi.org/10.1016/j.camwa.2006.04.013}, DOI={10.1016/j.camwa.2006.04.013}, number={8}, journal={Computers & Mathematics with Applications}, publisher={Elsevier BV}, author={Šarler, B. and Vertnik, R.}, year={2006}, month=apr, pages={1269–1282} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        21
      ]
    ],
    "date-time": "2025-08-21T06:16:40Z",
    "timestamp": 1755757000087
  },
  "reference-count": 23,
  "publisher": "Elsevier BV",
  "issue": "8",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2006,
            4,
            1
          ]
        ],
        "date-time": "2006-04-01T00:00:00Z",
        "timestamp": 1143849600000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://www.elsevier.com/tdm/userlicense/1.0/"
    },
    {
      "start": {
        "date-parts": [
          [
            2013,
            7,
            17
          ]
        ],
        "date-time": "2013-07-17T00:00:00Z",
        "timestamp": 1374019200000
      },
      "content-version": "vor",
      "delay-in-days": 2664,
      "URL": "https://www.elsevier.com/open-access/userlicense/1.0/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2006,
        4
      ]
    ]
  },
  "DOI": "10.1016/j.camwa.2006.04.013",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        7,
        18
      ]
    ],
    "date-time": "2006-07-18T11:13:15Z",
    "timestamp": 1153221195000
  },
  "page": "1269-1282",
  "source": "Crossref",
  "is-referenced-by-count": 307,
  "title": "Meshfree explicit local radial basis function collocation method for diffusion problems",
  "prefix": "10.1016",
  "volume": "51",
  "author": [
    {
      "given": "B.",
      "family": "\u0160arler",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "R.",
      "family": "Vertnik",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1016/j.camwa.2006.04.013_bib1",
      "series-title": "The Meshless Method",
      "author": "Atluri",
      "year": "2002"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib2",
      "series-title": "Mesh Free Methods",
      "author": "Liu",
      "year": "2003"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib3",
      "series-title": "The Meshless Method for Domain and BIE Discretisations",
      "author": "Atluri",
      "year": "2004"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib4",
      "series-title": "Advanced Numerical Methods in Heat Transfer",
      "first-page": "225",
      "article-title": "Chapter 9: \u201cMeshless Methods\u201d",
      "author": "\u0160arler",
      "year": "2004"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib5",
      "series-title": "Radial Basis Function: Theory and Implementations",
      "author": "Buhmann",
      "year": "2003"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib6",
      "doi-asserted-by": "crossref",
      "first-page": "147",
      "DOI": "10.1016/0898-1221(90)90271-K",
      "article-title": "Multiquadrics\u2014A scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to parabolic, hyperbolic and elliptic partial differential equations",
      "volume": "19",
      "author": "Kansa",
      "year": "1990",
      "journal-title": "Computers Math. Applic."
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib7",
      "series-title": "Surface Fitting and Multiresolution Methods",
      "first-page": "131",
      "article-title": "Solving partial differential equations by collocation with radial basis functions",
      "author": "Fasshauer",
      "year": "1997"
    },
    {
      "issue": "3\u20135",
      "key": "10.1016/j.camwa.2006.04.013_bib8",
      "doi-asserted-by": "crossref",
      "first-page": "551",
      "DOI": "10.1016/S0898-1221(01)00305-4",
      "article-title": "Comparison analysis between unsymmetric and symmetric RBFCMS for the numerical solution of PDEs",
      "volume": "43",
      "author": "Power",
      "year": "2002",
      "journal-title": "Computers Math. Applic."
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib9",
      "doi-asserted-by": "crossref",
      "first-page": "75",
      "DOI": "10.1007/978-3-642-56103-0_6",
      "article-title": "New RBF collocation schemes and kernel RBFs with applications",
      "volume": "26",
      "author": "Chen",
      "year": "2002",
      "journal-title": "Lecture Notes in Computational Science and Engineering"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib10",
      "first-page": "85",
      "article-title": "Indirect RBFN method with thin plate splines for numerical solution of differential equations",
      "volume": "4",
      "author": "Mai-Duy",
      "year": "2003",
      "journal-title": "Computer Modeling in Engineering & Sciences"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib11",
      "first-page": "185",
      "article-title": "A radial basis function collocation approach in computational fluid dynamics",
      "volume": "7",
      "author": "Sarler",
      "year": "2005",
      "journal-title": "Computer Modeling in Engineering & Sciences"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib12",
      "doi-asserted-by": "crossref",
      "first-page": "185",
      "DOI": "10.1016/S0893-6080(00)00095-2",
      "article-title": "Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks",
      "volume": "14",
      "author": "Mai-Duy",
      "year": "2001",
      "journal-title": "Neural Networks"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib13",
      "doi-asserted-by": "crossref",
      "first-page": "187",
      "DOI": "10.1108/09615530410513809",
      "article-title": "Radial basis function collocation method solution of natural convection in porous media",
      "volume": "14",
      "author": "Sarler",
      "year": "2004",
      "journal-title": "Int. J. Numer. Methods Heat & Fluid Flow"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib14",
      "first-page": "1",
      "article-title": "Solving the Stefan problem by the RBFCM",
      "volume": "44",
      "author": "Kova\u010devi\u0107",
      "year": "2003",
      "journal-title": "Numer. Heat Transfer, Part B: Fundamentals"
    },
    {
      "issue": "3\u20135",
      "key": "10.1016/j.camwa.2006.04.013_bib15",
      "doi-asserted-by": "crossref",
      "first-page": "359",
      "DOI": "10.1016/S0898-1221(01)00292-9",
      "article-title": "Multilevel compact radial basis functions based computational scheme for some elliptic problems",
      "volume": "43",
      "author": "Chen",
      "year": "2002",
      "journal-title": "Computers Math. Applic."
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib16",
      "doi-asserted-by": "crossref",
      "first-page": "133",
      "DOI": "10.1016/S0955-7997(01)00092-3",
      "article-title": "Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equations",
      "volume": "26",
      "author": "Mai-Duy",
      "year": "2002",
      "journal-title": "Engineering Analysis with Boundary Elements"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib17",
      "doi-asserted-by": "crossref",
      "first-page": "395",
      "DOI": "10.1007/s00466-003-0416-5",
      "article-title": "Local multiquadric approximation for solving boundary value problems",
      "volume": "30",
      "author": "Lee",
      "year": "2003",
      "journal-title": "Computational Mechanics"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib18",
      "doi-asserted-by": "crossref",
      "first-page": "68",
      "DOI": "10.1007/s00466-003-0501-9",
      "article-title": "On using radial basis functions in a \u201cfinite difference\u201d mode with applications to elasticity problems",
      "volume": "33",
      "author": "Tolstykh",
      "year": "2003",
      "journal-title": "Computational Mechanics"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib19",
      "doi-asserted-by": "crossref",
      "first-page": "941",
      "DOI": "10.1016/S0045-7825(02)00618-7",
      "article-title": "Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations",
      "volume": "192",
      "author": "Shu",
      "year": "2003",
      "journal-title": "Computer Methods in Applied Mechanics and Engineering"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib20",
      "series-title": "Benchmark Tests for Thermal Analysis",
      "author": "Cameron",
      "year": "1986"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib21",
      "doi-asserted-by": "crossref",
      "first-page": "1807",
      "DOI": "10.1002/nme.1620231003",
      "article-title": "Comparison of finite element techniques for solidification problems",
      "volume": "29",
      "author": "Dalhuijsen",
      "year": "1986",
      "journal-title": "International Journal for Numerical Methods in Engineering"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib22",
      "doi-asserted-by": "crossref",
      "first-page": "65",
      "DOI": "10.1016/S0955-7997(97)00113-6",
      "article-title": "Dual reciprocity boundary element method for convectioe-diffusive solid-liquid phase change problems, Part 2: Numerical examples",
      "volume": "21",
      "author": "Sarler",
      "year": "1998",
      "journal-title": "Engineering Analysis with Boundary Elements"
    },
    {
      "key": "10.1016/j.camwa.2006.04.013_bib23",
      "series-title": "Conduction of Heat in Solids",
      "author": "Carlsaw",
      "year": "1995"
    }
  ],
  "container-title": "Computers &amp; Mathematics with Applications",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0898122106000836?httpAccept=text/xml",
      "content-type": "text/xml",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0898122106000836?httpAccept=text/plain",
      "content-type": "text/plain",
      "content-version": "vor",
      "intended-application": "text-mining"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        1,
        15
      ]
    ],
    "date-time": "2019-01-15T02:21:04Z",
    "timestamp": 1547518864000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S0898122106000836"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2006,
        4
      ]
    ]
  },
  "references-count": 23,
  "journal-issue": {
    "issue": "8",
    "published-print": {
      "date-parts": [
        [
          2006,
          4
        ]
      ]
    }
  },
  "alternative-id": [
    "S0898122106000836"
  ],
  "URL": "http://dx.doi.org/10.1016/j.camwa.2006.04.013",
  "relation": {},
  "ISSN": [
    "0898-1221"
  ],
  "subject": [],
  "container-title-short": "Computers &amp; Mathematics with Applications",
  "published": {
    "date-parts": [
      [
        2006,
        4
      ]
    ]
  }
}