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Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator

Please always quote using this URN: urn:nbn:de:bvb:20-opus-158525
  • An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numericalAn efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.show moreshow less

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Metadaten
Author: Duncan Kioi Gathungu, Alfio Borzì
URN:urn:nbn:de:bvb:20-opus-158525
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Language:English
Parent Title (English):Applied Mathematics
Year of Completion:2017
Volume:8
Issue:7
Pagenumber:967-986
Source:Applied Mathematics , 8(7), 967-986 (2017). DOI: 10.4236/am.2017.87076
DOI:https://doi.org/10.4236/am.2017.87076
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik
Tag:elliptic problems; finite differences; fredholm operator; multigrid schemes; numerical analysis
Release Date:2018/03/23
EU-Project number / Contract (GA) number:304617
OpenAIRE:OpenAIRE
Collections:Open-Access-Publikationsfonds / Förderzeitraum 2017
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International