hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Algebraic multigrid for complex symmetric matrices and applications
Journal of Computational and Applied Mathematics
An Introduction to Algebraic Multigrid
Computing in Science and Engineering
Journal of Computational and Applied Mathematics
On the utilization of edge matrices in algebraic multigrid
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
An Algebraic Multigrid Method with Guaranteed Convergence Rate
SIAM Journal on Scientific Computing
A hybrid multigrid method for convection-diffusion problems
Journal of Computational and Applied Mathematics
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We propose a new general algorithm for constructing interpolation weights in algebraic multigrid (AMG). It exploits a proper extension mapping outside a neighborhood about a fine degree of freedom (dof) to be interpolated. The extension mapping provides boundary values (based on the coarse dofs used to perform the interpolation) at the boundary of the neighborhood. The interpolation value is then obtained by matrix dependent harmonic extension of the boundary values into the interior of the neighborhood.We describe the method, present examples of useful extension operators, provide a two-grid analysis of model problems, and, by way of numerical experiments, demonstrate the successful application of the method to discretized elliptic problems.