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Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator
Institut für Mathematik, Universität Würzburg, Würzburg, Germany
Institut für Mathematik, Universität Würzburg, Würzburg, Germany
- 1 Institut für Mathematik, Universität Würzburg, Würzburg, Germany
- 2 Institut für Mathematik, Universität Würzburg, Würzburg, Germany
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Abstract
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 numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.
KeywordsElliptic ProblemsFredholm OperatorMultigrid SchemesFinite DifferencesNumerical Analysis
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