Algebraic Multigrid for Problems in Linear Elasticity discretized by DG methods

MSc Erwin Karer

May 26, 2009, 3:30 p.m. MZ 005B

In this talk we will focus on linear elasticity problems using a discontinuous Galerkin discretization, which is robust with respect to the Poisson ratio ν in the limit case of incompressible materials, i.e., $ν
ightarrow 1/2$. Those formulations can be rewritten in terms of a sum over face contributions, which is the starting point for our method. First of all we will consider two space dimensions.

In order to construct an efficient preconditioner for the system matrix, we split the set of elements into two independent sets. First, we eliminate the degrees of freedom of one set. Then we apply a transformation of the remaining matrix in order to get a hierarchical representation. This representation is further used to set up a two-level method, were the coarse-grid matrix is obtained by an assembling of local “algebraic edge” matrices.