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.…
Author: | Duncan Kioi Gathungu, Alfio Borzì |
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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): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |