Volume 39, pp. 333-339, 2012.

Cascadic multigrid preconditioner for elliptic equations with jump coefficients

Zhiyong Liu and Yinnian He


This paper provides a proof of robustness of the cascadic multigrid preconditioner for the linear finite element approximation of second order elliptic problems with strongly discontinuous coefficients. As a result, we prove that the convergence rate of the conjugate gradient method with cascadic multigrid preconditioner is uniform with respect to large jumps and mesh sizes.

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Key words

Jump coefficients, conjugate gradient, condition number, cascadic multigrid.

AMS subject classifications

65N30, 65N55, 65F10

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