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

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Document pages: 20 pages

Abstract: An efficient multigrid finite-differences scheme for solving elliptic Fredholmpartial integro-differential equations (PIDE) is discussed. This scheme combinesa second-order accurate finite difference discretization of the PIDEproblem with a multigrid scheme that includes a fast multilevel integration ofthe Fredholm operator allowing the fast solution of the PIDE problem. Theoreticalestimates of second-order accuracy and results of local Fourier analysisof convergence of the proposed multigrid scheme are presented. Results ofnumerical experiments validate these estimates and demonstrate optimal computationalcomplexity of the proposed framework.

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