An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations

Reference:

Boonen, T., Van Lent, J. and Vandewalle, S., 2009. An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations. Applied Numerical Mathematics, 59 (3-4), pp. 507-521.

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Official URL:

http://dx.doi.org/10.1016/j.apnum.2008.03.004

Abstract

We present in algebraic multigrid algorithm for fully Coupled implicit Runge-Kutta and Boundary Value Method time-discretizations of the div-grad and curl-curl equations. The algorithm uses a blocksmoother and a multigrid hierarchy derived from the hierarchy built by any algebraic multigrid algorithm for the stationary version of the problem. By a theoretical analysis and numerical experiments, we show that the convergence is similar to or better than the convergence of the scalar algebraic multigrid algorithm on which it is based. The algorithm benefits from several possibilities for implementation optimization. This results in a Computational complexity which, for a modest number of stages, scales almost linearly its a function of the munber of variables. (

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