Multigrid finite element methods on semi-structured triangular grids for planar elasticity

Abstract

Multigrid methods for a stencil-based implementation of a finite element method for planar elasticity, using semi-structured triangular grids, are presented. Local Fourier analysis (LFA) is applied to identify the correct multigrid components. To this end, LFA for multigrid methods on regular triangular grids is extended to the case of the problem of planar elasticity, although its application to other systems is straightforward. For the discrete elasticity operator obtained with linear finite elements, different collective smoothers, such as three-color smoother and some zebra-type smoothers, are analyzed, and LFA results for these smoothers are shown. The multigrid method is constructed in a block-wise form. In particular, different smoothers and different numbers of pre- and post-smoothing steps are considered in each triangle of the coarsest triangulation of the domain. Some numerical experiments are presented to illustrate the efficiency of this multigrid algorithm. © 2009 John Wiley & Sons, Ltd.