DOI: 10.1006/acha.2000.0310. Spectral Approximation of the Free-Space Heat Kernel

Spectral Approximation of the Free-Space Heat Kernel

10.1006/acha.2000.0310

Crossref journal-article

Elsevier BV

Applied and Computational Harmonic Analysis (78)

Bibliography

Greengard, L., & Lin, P. (2000). Spectral Approximation of the Free-Space Heat Kernel. Applied and Computational Harmonic Analysis, 9(1), 83â97.

Authors 2

Leslie Greengard (first)
Patrick Lin (additional)

References 23 Referenced 63

{'key': '10.1006/acha.2000.0310_RF1', 'series-title': 'Handbook of Mathematical Functions', 'year': '1965'} / Handbook of Mathematical Functions (1965)
10.1006/acha.1995.1026 / Appl. Comput. Harmon. Anal. / On the fast Fourier transform of functions with singularities by Beylkin (1995)
10.1137/0152075 / SIAM J. Appl. Math. / Numerical simulations of unsteady crystal growth by Brattkus (1992)
{'key': '10.1006/acha.2000.0310_RF4', 'series-title': 'Topics in Boundary Element Research', 'year': '1981'} / Topics in Boundary Element Research (1981)
{'key': '10.1006/acha.2000.0310_RF5', 'series-title': 'Layer Potentials and Boundary Value problems for the Heat Equation on Lipschitz Cylinders', 'author': 'Brown', 'year': '1987'} / Layer Potentials and Boundary Value problems for the Heat Equation on Lipschitz Cylinders by Brown (1987)
{'key': '10.1006/acha.2000.0310_RF6', 'series-title': 'Methods of Numerical Integration', 'author': 'Davis', 'year': '1967'} / Methods of Numerical Integration by Davis (1967)
A. Dutt, and, V. Rokhlin, On the rapid evaluation of trigonometric series, Research Report, 893, Yale Computer Science Department, 1992. (10.21236/ADA249029)
{'key': '10.1006/acha.2000.0310_RF8', 'series-title': 'Fourier Series and Integrals', 'author': 'Dym', 'year': '1972'} / Fourier Series and Integrals by Dym (1972)
{'key': '10.1006/acha.2000.0310_RF9', 'series-title': 'Partial Differential Equations of Parabolic Type', 'author': 'Friedman', 'year': '1964'} / Partial Differential Equations of Parabolic Type by Friedman (1964)
10.1137/0912004 / SIAM J. Sci. Stat. Comput. / The fast Gauss transform by Greengard (1991)
10.1002/cpa.3160430802 / Comm. Pure Appl. Math. / The fast algorithm for the evaluation of heat potentials by Greengard (1990)
{'key': '10.1006/acha.2000.0310_RF12', 'series-title': 'Partial Differential Equations of Mathematical Physics and Integral Equations', 'author': 'Guenther', 'year': '1988'} / Partial Differential Equations of Mathematical Physics and Integral Equations by Guenther (1988)
10.2307/1967695 / Ann. of Math. / A class of reciprocal functions by Hill (1926)
{'key': '10.1006/acha.2000.0310_RF14', 'series-title': 'Direct Numerical Simulations of Unsteady Separated Flows Using Vortex Methods', 'author': 'Koumoutsakos', 'year': '1993'} / Direct Numerical Simulations of Unsteady Separated Flows Using Vortex Methods by Koumoutsakos (1993)
{'key': '10.1006/acha.2000.0310_RF15', 'series-title': 'On the Numerical Solution of the Heat Equation in Unbounded Domains', 'author': 'Lin', 'year': '1993'} / On the Numerical Solution of the Heat Equation in Unbounded Domains by Lin (1993)
10.1090/S0025-5718-1986-0815832-6 / Math. Comp. / Boundary integral solutions of the heat equation by McIntyre (1986)
{'key': '10.1006/acha.2000.0310_RF17', 'series-title': 'Integral Equations', 'author': 'Mikhlin', 'year': '1957'} / Integral Equations by Mikhlin (1957)
{'key': '10.1006/acha.2000.0310_RF18', 'series-title': 'Boundary Integral Methods: Theory and Applications', 'year': '1990'} / Boundary Integral Methods: Theory and Applications (1990)
{'key': '10.1006/acha.2000.0310_RF19', 'series-title': 'The Single Layer Heat Potential and Galerkin Boundary Element Methods for the Heat Equation', 'author': 'Noon', 'year': '1988'} / The Single Layer Heat Potential and Galerkin Boundary Element Methods for the Heat Equation by Noon (1988)
{'key': '10.1006/acha.2000.0310_RF20', 'series-title': 'Integral Equations and Their Applications', 'author': 'Pogorzelski', 'year': '1966'} / Integral Equations and Their Applications by Pogorzelski (1966)
10.1016/0021-9991(92)90140-T / J. Comput. Phys. / Crystal growth and dendritic solidification by Sethian (1992)
10.1016/0021-9991(92)90206-E / J. Comput. Phys. / Fast potential theory II. Layer potentials and discrete sums by Strain (1992)
10.1137/0915013 / SIAM J. Sci. Comput. / Fast adaptive methods for the free-space heat equation by Strain (1992)

Dates

Type	When
Created	22 years, 11 months ago (Sept. 16, 2002, 9:49 a.m.)
Deposited	4 years, 3 months ago (May 3, 2021, 12:50 a.m.)
Indexed	3 months, 3 weeks ago (May 5, 2025, 10:30 a.m.)
Issued	25 years, 2 months ago (July 1, 2000)
Published	25 years, 2 months ago (July 1, 2000)
Published Print	25 years, 2 months ago (July 1, 2000)

Funders 0

None

BibTeX

@article{Greengard_2000, title={Spectral Approximation of the Free-Space Heat Kernel}, volume={9}, ISSN={1063-5203}, url={http://dx.doi.org/10.1006/acha.2000.0310}, DOI={10.1006/acha.2000.0310}, number={1}, journal={Applied and Computational Harmonic Analysis}, publisher={Elsevier BV}, author={Greengard, Leslie and Lin, Patrick}, year={2000}, month=jul, pages={83–97} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        5,
        5
      ]
    ],
    "date-time": "2025-05-05T14:30:18Z",
    "timestamp": 1746455418145
  },
  "reference-count": 23,
  "publisher": "Elsevier BV",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2000,
            7,
            1
          ]
        ],
        "date-time": "2000-07-01T00:00:00Z",
        "timestamp": 962409600000
      },
      "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": 4764,
      "URL": "https://www.elsevier.com/open-access/userlicense/1.0/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2000,
        7
      ]
    ]
  },
  "DOI": "10.1006/acha.2000.0310",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        9,
        16
      ]
    ],
    "date-time": "2002-09-16T13:49:45Z",
    "timestamp": 1032184185000
  },
  "page": "83-97",
  "source": "Crossref",
  "is-referenced-by-count": 63,
  "title": "Spectral Approximation of the Free-Space Heat Kernel",
  "prefix": "10.1006",
  "volume": "9",
  "author": [
    {
      "given": "Leslie",
      "family": "Greengard",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Patrick",
      "family": "Lin",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1006/acha.2000.0310_RF1",
      "series-title": "Handbook of Mathematical Functions",
      "year": "1965"
    },
    {
      "key": "10.1006/acha.2000.0310_RF2",
      "doi-asserted-by": "crossref",
      "first-page": "363",
      "DOI": "10.1006/acha.1995.1026",
      "article-title": "On the fast Fourier transform of functions with singularities",
      "volume": "2",
      "author": "Beylkin",
      "year": "1995",
      "journal-title": "Appl. Comput. Harmon. Anal."
    },
    {
      "key": "10.1006/acha.2000.0310_RF3",
      "doi-asserted-by": "crossref",
      "first-page": "1303",
      "DOI": "10.1137/0152075",
      "article-title": "Numerical simulations of unsteady crystal growth",
      "volume": "52",
      "author": "Brattkus",
      "year": "1992",
      "journal-title": "SIAM J. Appl. Math."
    },
    {
      "key": "10.1006/acha.2000.0310_RF4",
      "series-title": "Topics in Boundary Element Research",
      "year": "1981"
    },
    {
      "key": "10.1006/acha.2000.0310_RF5",
      "series-title": "Layer Potentials and Boundary Value problems for the Heat Equation on Lipschitz Cylinders",
      "author": "Brown",
      "year": "1987"
    },
    {
      "key": "10.1006/acha.2000.0310_RF6",
      "series-title": "Methods of Numerical Integration",
      "author": "Davis",
      "year": "1967"
    },
    {
      "key": "10.1006/acha.2000.0310_RF7",
      "doi-asserted-by": "crossref",
      "unstructured": "A. Dutt, and, V. Rokhlin, On the rapid evaluation of trigonometric series, Research Report, 893, Yale Computer Science Department, 1992.",
      "DOI": "10.21236/ADA249029"
    },
    {
      "key": "10.1006/acha.2000.0310_RF8",
      "series-title": "Fourier Series and Integrals",
      "author": "Dym",
      "year": "1972"
    },
    {
      "key": "10.1006/acha.2000.0310_RF9",
      "series-title": "Partial Differential Equations of Parabolic Type",
      "author": "Friedman",
      "year": "1964"
    },
    {
      "key": "10.1006/acha.2000.0310_RF10",
      "doi-asserted-by": "crossref",
      "first-page": "79",
      "DOI": "10.1137/0912004",
      "article-title": "The fast Gauss transform",
      "volume": "12",
      "author": "Greengard",
      "year": "1991",
      "journal-title": "SIAM J. Sci. Stat. Comput."
    },
    {
      "key": "10.1006/acha.2000.0310_RF11",
      "doi-asserted-by": "crossref",
      "first-page": "949",
      "DOI": "10.1002/cpa.3160430802",
      "article-title": "The fast algorithm for the evaluation of heat potentials",
      "volume": "43",
      "author": "Greengard",
      "year": "1990",
      "journal-title": "Comm. Pure Appl. Math."
    },
    {
      "key": "10.1006/acha.2000.0310_RF12",
      "series-title": "Partial Differential Equations of Mathematical Physics and Integral Equations",
      "author": "Guenther",
      "year": "1988"
    },
    {
      "key": "10.1006/acha.2000.0310_RF13",
      "doi-asserted-by": "crossref",
      "first-page": "427",
      "DOI": "10.2307/1967695",
      "article-title": "A class of reciprocal functions",
      "volume": "27",
      "author": "Hill",
      "year": "1926",
      "journal-title": "Ann. of Math."
    },
    {
      "key": "10.1006/acha.2000.0310_RF14",
      "series-title": "Direct Numerical Simulations of Unsteady Separated Flows Using Vortex Methods",
      "author": "Koumoutsakos",
      "year": "1993"
    },
    {
      "key": "10.1006/acha.2000.0310_RF15",
      "series-title": "On the Numerical Solution of the Heat Equation in Unbounded Domains",
      "author": "Lin",
      "year": "1993"
    },
    {
      "key": "10.1006/acha.2000.0310_RF16",
      "doi-asserted-by": "crossref",
      "first-page": "71",
      "DOI": "10.1090/S0025-5718-1986-0815832-6",
      "article-title": "Boundary integral solutions of the heat equation",
      "volume": "46",
      "author": "McIntyre",
      "year": "1986",
      "journal-title": "Math. Comp."
    },
    {
      "key": "10.1006/acha.2000.0310_RF17",
      "series-title": "Integral Equations",
      "author": "Mikhlin",
      "year": "1957"
    },
    {
      "key": "10.1006/acha.2000.0310_RF18",
      "series-title": "Boundary Integral Methods: Theory and Applications",
      "year": "1990"
    },
    {
      "key": "10.1006/acha.2000.0310_RF19",
      "series-title": "The Single Layer Heat Potential and Galerkin Boundary Element Methods for the Heat Equation",
      "author": "Noon",
      "year": "1988"
    },
    {
      "key": "10.1006/acha.2000.0310_RF20",
      "series-title": "Integral Equations and Their Applications",
      "author": "Pogorzelski",
      "year": "1966"
    },
    {
      "key": "10.1006/acha.2000.0310_RF21",
      "doi-asserted-by": "crossref",
      "first-page": "231",
      "DOI": "10.1016/0021-9991(92)90140-T",
      "article-title": "Crystal growth and dendritic solidification",
      "volume": "98",
      "author": "Sethian",
      "year": "1992",
      "journal-title": "J. Comput. Phys."
    },
    {
      "key": "10.1006/acha.2000.0310_RF22",
      "doi-asserted-by": "crossref",
      "first-page": "251",
      "DOI": "10.1016/0021-9991(92)90206-E",
      "article-title": "Fast potential theory II. Layer potentials and discrete sums",
      "volume": "99",
      "author": "Strain",
      "year": "1992",
      "journal-title": "J. Comput. Phys."
    },
    {
      "key": "10.1006/acha.2000.0310_RF23",
      "doi-asserted-by": "crossref",
      "first-page": "185",
      "DOI": "10.1137/0915013",
      "article-title": "Fast adaptive methods for the free-space heat equation",
      "volume": "15",
      "author": "Strain",
      "year": "1992",
      "journal-title": "SIAM J. Sci. Comput."
    }
  ],
  "container-title": "Applied and Computational Harmonic Analysis",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.elsevier.com/content/article/PII:S1063520300903105?httpAccept=text/xml",
      "content-type": "text/xml",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://api.elsevier.com/content/article/PII:S1063520300903105?httpAccept=text/plain",
      "content-type": "text/plain",
      "content-version": "vor",
      "intended-application": "text-mining"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2021,
        5,
        3
      ]
    ],
    "date-time": "2021-05-03T04:50:39Z",
    "timestamp": 1620017439000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S1063520300903105"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2000,
        7
      ]
    ]
  },
  "references-count": 23,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          2000,
          7
        ]
      ]
    }
  },
  "alternative-id": [
    "S1063520300903105"
  ],
  "URL": "http://dx.doi.org/10.1006/acha.2000.0310",
  "relation": {},
  "ISSN": [
    "1063-5203"
  ],
  "subject": [],
  "container-title-short": "Applied and Computational Harmonic Analysis",
  "published": {
    "date-parts": [
      [
        2000,
        7
      ]
    ]
  }
}