Local Fourier analysis (LFA) is a classical tool for proving convergence theorems for multigrid methods (MGMs). Analogously, the symbols of the involved matrices are studied to prove convergence results for MGMs for Toeplitz matrices. We show that in the case of elliptic partial differential equations (PDEs) with constant coefficients, the two different approaches lead to an equivalent optimality condition. We argue that the analysis for Toeplitz matrices is an algebraic generalization of the LFA which allows to deal not only with differential problems but also, e.g., with integral problems. A class of grid transfer operators related to the B-spline's refinement equation is discussed as well.

Grid transfer operators for multigrid methods

DONATELLI, MARCO
2011-01-01

Abstract

Local Fourier analysis (LFA) is a classical tool for proving convergence theorems for multigrid methods (MGMs). Analogously, the symbols of the involved matrices are studied to prove convergence results for MGMs for Toeplitz matrices. We show that in the case of elliptic partial differential equations (PDEs) with constant coefficients, the two different approaches lead to an equivalent optimality condition. We argue that the analysis for Toeplitz matrices is an algebraic generalization of the LFA which allows to deal not only with differential problems but also, e.g., with integral problems. A class of grid transfer operators related to the B-spline's refinement equation is discussed as well.
2011
Donatelli, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1736448
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