Fast iterative solvers for thin structures

For very large systems of equations arising from 3D finite element formulation, pre-conditioned iterative solvers are preferred over direct solvers due to their reduced memory requirements. However, in the finite-element analysis of thin structures such as beam and plate structures, iterative solvers perform poorly due to the presence of poor quality elements. In particular, their efficiency drops significantly with increase in the aspect ratio of such structures. s paper, we propose a dual-representation based multi-grid framework for efficient iterative analysis of thin structures. The proposed iterative solvers are relatively insensitive to the quality of the elements since they exploit classical beam and plate theories to spectrally complement 3D finite element analysis. This leads to significant computational gains, as supported by the numerical experiments.