Improved Quadrature Formula for a Single-Layer Potential

An improved quadrature formula is derived for a single-layer potential with a smooth density given on a closed or open surface. The formula ensures a uniform approximation of the potential near the surface and preserves the continuity of the potential as the observation point tends to the surface fr...

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Published inComputational mathematics and mathematical physics Vol. 63; no. 2; pp. 187 - 201
Main Authors Krutitskii, P. A., Reznichenko, I. O.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.02.2023
Springer Nature B.V
Subjects
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ISSN0965-5425
1555-6662
DOI10.1134/S0965542523020100

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Abstract An improved quadrature formula is derived for a single-layer potential with a smooth density given on a closed or open surface. The formula ensures a uniform approximation of the potential near the surface and preserves the continuity of the potential as the observation point tends to the surface from inside the domain. These properties are confirmed by numerical tests. For the potential computed near the surface, the present quadrature formula yields higher accuracy than previously known quadrature rules, which is also confirmed by numerical tests. Additionally, a quadrature formula for the direct value of the single-layer potential on the surface is derived. Numerical tests conducted with this formula confirm its efficiency and accuracy.
AbstractList An improved quadrature formula is derived for a single-layer potential with a smooth density given on a closed or open surface. The formula ensures a uniform approximation of the potential near the surface and preserves the continuity of the potential as the observation point tends to the surface from inside the domain. These properties are confirmed by numerical tests. For the potential computed near the surface, the present quadrature formula yields higher accuracy than previously known quadrature rules, which is also confirmed by numerical tests. Additionally, a quadrature formula for the direct value of the single-layer potential on the surface is derived. Numerical tests conducted with this formula confirm its efficiency and accuracy.
Author Reznichenko, I. O.
Krutitskii, P. A.
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  givenname: I. O.
  surname: Reznichenko
  fullname: Reznichenko, I. O.
  email: io.reznichenko@physics.msu.ru
  organization: Faculty of Physics, Lomonosov Moscow State University
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Cites_doi 10.1134/S0012266119090106
10.32917/hmj/1206126877
10.1080/00036819608840484
10.1134/S0012266116090135
10.1007/978-3-642-48860-3
10.4171/ZAA/827
10.1093/imamat/60.3.285
10.1007/s10665-006-9058-x
10.4171/ZAA/788
10.1090/S0033-569X-08-01117-4
10.1155/S0161171298000301
ContentType Journal Article
Copyright Pleiades Publishing, Ltd. 2023. ISSN 0965-5425, Computational Mathematics and Mathematical Physics, 2023, Vol. 63, No. 2, pp. 187–201. © Pleiades Publishing, Ltd., 2023. Russian Text © The Author(s), 2023, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2023, Vol. 63, No. 2, pp. 230–244.
Pleiades Publishing, Ltd. 2023.
Copyright_xml – notice: Pleiades Publishing, Ltd. 2023. ISSN 0965-5425, Computational Mathematics and Mathematical Physics, 2023, Vol. 63, No. 2, pp. 187–201. © Pleiades Publishing, Ltd., 2023. Russian Text © The Author(s), 2023, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2023, Vol. 63, No. 2, pp. 230–244.
– notice: Pleiades Publishing, Ltd. 2023.
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References PrudnikovA. P.BrychkovYu. A.MarichevO. I.Integrals and Series1986New YorkGordon and Breach0606.33001
KrutitskiiP. A.The 2-dimensional Dirichlet problem in an external domain with cutsZ. Anal. Anwend.199817361378163255110.4171/ZAA/8270907.35036
KrutitskiiP. A.The Neumann problem on wave propagation in a 2-D external domain with cutsJ. Math. Kyoto Univ.19983843945216612040948.35031
KrutitskiiP. A.The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curvesInt. J. Math. Math. Sci.199821209216160970810.1155/S01611712980003010910.35040
V. A. Il’in and E. G. Poznyak, Fundamentals of Calculus (Fizmatlit, Moscow, 1973), Part 2 [in Russian].
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1999; Dover, New York, 2011).
ColtonD.KressR.Integral Equation Methods in Scattering Theory1984New YorkWiley0522.35001
KrutitskiiP. A.FedotovA. D.KolybasovaV. V.Quadrature formula for the simple layer potentialDiffer. Equations20195512261241402804410.1134/S00122661190901061455.65040
ButuzovV. F.KrutitskayaN. Ch.MedvedevG. N.ShishkinA. A.Calculus in Questions and Problems2000MoscowFizmatlit1029.00002
BrebbiaC. A.TellesJ. C. F.WrobelL. C.Boundary Element Techniques: Theory and Applications in Engineering1984BerlinSpringer-Verlag10.1007/978-3-642-48860-30556.73086
P. A. Krutitskii, A. D. Fedotov, and V. V. Kolybasova, Preprint No. 112, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 2019).
KrutitskiiP. A.The Dirichlet problem for the dissipative Helmholtz equation in a plane domain bounded by closed and open curvesHiroshima Math. J.199828149168161283810.32917/hmj/12061268770909.35036
KrutitskiiP. A.The Helmholtz equation in the exterior of slits in a plane with different impedance boundary conditions on opposite sides of the slitsQ. Appl. Math.2009677392249507210.1090/S0033-569X-08-01117-41163.35342
GuntherN. M.Potential Theory and Its Application to the Fundamental Problems of Mathematical Physics1967New YorkUngar
KrutitskiiP. A.The skew derivative problem in the exterior of open curves in a planeZ. Anal. Anwend.199716739747147272810.4171/ZAA/7880888.35027
KrutitskiiP. A.Wave propagation in a 2-D external domain with cutsAppl. Anal.199662297309162350710.1080/000368196088404840857.73023
VladimirovV. S.Equations of Mathematical Physics1971New YorkMarcel Dekker0231.35002
KrutitskiiP. A.KwakD. Y.HyonY. K.Numerical treatment of a skew-derivative problem for the Laplace equation in the exterior of an open arcJ. Eng. Math.2007592560234276810.1007/s10665-006-9058-x1126.78018
KrutitskiiP. A.KolybasovaV. V.Numerical method for the solution of integral equations in a problem with directional derivative for the Laplace equation outside open curvesDiffer. Equations20165212191233356362610.1134/S00122661160901351357.65321
KrutitskiiP. A.On the electric current from electrodes in a magnetized semiconductor filmIMA J. Appl. Math.199860285297165386310.1093/imamat/60.3.2850915.35100
1771_CR6
P. A. Krutitskii (1771_CR15) 1996; 62
V. F. Butuzov (1771_CR17) 2000
P. A. Krutitskii (1771_CR13) 1998; 60
1771_CR1
P. A. Krutitskii (1771_CR11) 1998; 28
N. M. Gunther (1771_CR2) 1967
P. A. Krutitskii (1771_CR9) 1998; 17
P. A. Krutitskii (1771_CR14) 1998; 38
P. A. Krutitskii (1771_CR8) 2016; 52
P. A. Krutitskii (1771_CR12) 1998; 21
D. Colton (1771_CR3) 1984
P. A. Krutitskii (1771_CR10) 1997; 16
P. A. Krutitskii (1771_CR16) 2009; 67
V. S. Vladimirov (1771_CR19) 1971
P. A. Krutitskii (1771_CR5) 2019; 55
1771_CR18
A. P. Prudnikov (1771_CR20) 1986
C. A. Brebbia (1771_CR4) 1984
P. A. Krutitskii (1771_CR7) 2007; 59
References_xml – reference: A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1999; Dover, New York, 2011).
– reference: KrutitskiiP. A.The 2-dimensional Dirichlet problem in an external domain with cutsZ. Anal. Anwend.199817361378163255110.4171/ZAA/8270907.35036
– reference: KrutitskiiP. A.The Neumann problem on wave propagation in a 2-D external domain with cutsJ. Math. Kyoto Univ.19983843945216612040948.35031
– reference: BrebbiaC. A.TellesJ. C. F.WrobelL. C.Boundary Element Techniques: Theory and Applications in Engineering1984BerlinSpringer-Verlag10.1007/978-3-642-48860-30556.73086
– reference: KrutitskiiP. A.The Dirichlet problem for the dissipative Helmholtz equation in a plane domain bounded by closed and open curvesHiroshima Math. J.199828149168161283810.32917/hmj/12061268770909.35036
– reference: KrutitskiiP. A.KolybasovaV. V.Numerical method for the solution of integral equations in a problem with directional derivative for the Laplace equation outside open curvesDiffer. Equations20165212191233356362610.1134/S00122661160901351357.65321
– reference: GuntherN. M.Potential Theory and Its Application to the Fundamental Problems of Mathematical Physics1967New YorkUngar
– reference: V. A. Il’in and E. G. Poznyak, Fundamentals of Calculus (Fizmatlit, Moscow, 1973), Part 2 [in Russian].
– reference: P. A. Krutitskii, A. D. Fedotov, and V. V. Kolybasova, Preprint No. 112, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 2019).
– reference: ColtonD.KressR.Integral Equation Methods in Scattering Theory1984New YorkWiley0522.35001
– reference: KrutitskiiP. A.KwakD. Y.HyonY. K.Numerical treatment of a skew-derivative problem for the Laplace equation in the exterior of an open arcJ. Eng. Math.2007592560234276810.1007/s10665-006-9058-x1126.78018
– reference: VladimirovV. S.Equations of Mathematical Physics1971New YorkMarcel Dekker0231.35002
– reference: KrutitskiiP. A.The skew derivative problem in the exterior of open curves in a planeZ. Anal. Anwend.199716739747147272810.4171/ZAA/7880888.35027
– reference: KrutitskiiP. A.On the electric current from electrodes in a magnetized semiconductor filmIMA J. Appl. Math.199860285297165386310.1093/imamat/60.3.2850915.35100
– reference: KrutitskiiP. A.Wave propagation in a 2-D external domain with cutsAppl. Anal.199662297309162350710.1080/000368196088404840857.73023
– reference: KrutitskiiP. A.The Helmholtz equation in the exterior of slits in a plane with different impedance boundary conditions on opposite sides of the slitsQ. Appl. Math.2009677392249507210.1090/S0033-569X-08-01117-41163.35342
– reference: KrutitskiiP. A.FedotovA. D.KolybasovaV. V.Quadrature formula for the simple layer potentialDiffer. Equations20195512261241402804410.1134/S00122661190901061455.65040
– reference: ButuzovV. F.KrutitskayaN. Ch.MedvedevG. N.ShishkinA. A.Calculus in Questions and Problems2000MoscowFizmatlit1029.00002
– reference: KrutitskiiP. A.The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curvesInt. J. Math. Math. Sci.199821209216160970810.1155/S01611712980003010910.35040
– reference: PrudnikovA. P.BrychkovYu. A.MarichevO. I.Integrals and Series1986New YorkGordon and Breach0606.33001
– volume: 55
  start-page: 1226
  year: 2019
  ident: 1771_CR5
  publication-title: Differ. Equations
  doi: 10.1134/S0012266119090106
– volume: 28
  start-page: 149
  year: 1998
  ident: 1771_CR11
  publication-title: Hiroshima Math. J.
  doi: 10.32917/hmj/1206126877
– volume: 62
  start-page: 297
  year: 1996
  ident: 1771_CR15
  publication-title: Appl. Anal.
  doi: 10.1080/00036819608840484
– volume-title: Calculus in Questions and Problems
  year: 2000
  ident: 1771_CR17
– ident: 1771_CR6
– volume: 52
  start-page: 1219
  year: 2016
  ident: 1771_CR8
  publication-title: Differ. Equations
  doi: 10.1134/S0012266116090135
– volume-title: Boundary Element Techniques: Theory and Applications in Engineering
  year: 1984
  ident: 1771_CR4
  doi: 10.1007/978-3-642-48860-3
– volume-title: Integrals and Series
  year: 1986
  ident: 1771_CR20
– volume-title: Potential Theory and Its Application to the Fundamental Problems of Mathematical Physics
  year: 1967
  ident: 1771_CR2
– volume: 17
  start-page: 361
  year: 1998
  ident: 1771_CR9
  publication-title: Z. Anal. Anwend.
  doi: 10.4171/ZAA/827
– volume: 60
  start-page: 285
  year: 1998
  ident: 1771_CR13
  publication-title: IMA J. Appl. Math.
  doi: 10.1093/imamat/60.3.285
– ident: 1771_CR1
– volume: 59
  start-page: 25
  year: 2007
  ident: 1771_CR7
  publication-title: J. Eng. Math.
  doi: 10.1007/s10665-006-9058-x
– volume-title: Equations of Mathematical Physics
  year: 1971
  ident: 1771_CR19
– volume: 38
  start-page: 439
  year: 1998
  ident: 1771_CR14
  publication-title: J. Math. Kyoto Univ.
– volume: 16
  start-page: 739
  year: 1997
  ident: 1771_CR10
  publication-title: Z. Anal. Anwend.
  doi: 10.4171/ZAA/788
– ident: 1771_CR18
– volume-title: Integral Equation Methods in Scattering Theory
  year: 1984
  ident: 1771_CR3
– volume: 67
  start-page: 73
  year: 2009
  ident: 1771_CR16
  publication-title: Q. Appl. Math.
  doi: 10.1090/S0033-569X-08-01117-4
– volume: 21
  start-page: 209
  year: 1998
  ident: 1771_CR12
  publication-title: Int. J. Math. Math. Sci.
  doi: 10.1155/S0161171298000301
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Snippet An improved quadrature formula is derived for a single-layer potential with a smooth density given on a closed or open surface. The formula ensures a uniform...
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SubjectTerms Accuracy
Boundary value problems
Computational Mathematics and Numerical Analysis
General Numerical Methods
Helmholtz equations
Integral equations
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Quadratures
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Title Improved Quadrature Formula for a Single-Layer Potential
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