On a parallel multilevel solver for linear elasticity problems (Q2760351)

The author applies the additive multilevel iteration method to parallelly solving large scale linear elasticity problems. The method is based on a finite sequence \(\{T^i\}\) of three-dimensional meshes consisting of prisms. The meshes are constructed as tensor product of a fixed one-dimensional grid \(T_z\) and a sequence of nested two-dimensional triangulations \(T_{xy}^i\). The linear elasticity operator is approximated by a simpler elliptic operator splitted into an \(xy\)-plane part and a \(z\)-direction part. By means of a hierarchical basis related to \(\{T^i\}\), the author introduces stiffness matrices \(Q^i\) reflecting the splitting. Then an \(i\)-dependent iterative two-level preconditioner to \(Q^i\) as well as its multilevel modification are presented, and optimality conditions for the proposed method are investigated. After a brief comment on parallelization, attention is paid to model problems arising from bridge foundation modeling. Finally, the author describes the parallel performance of the solver on Cray T3E-600 and Sun ES/4000 computer systems.