Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses

This paper is concerned with optimization techniques for the iterative solution of sparse linear systems arising from finite element discretization of partial differential equations. Three different data structures are used to store the coefficient matrices: the usual element-based data structure, the compressed storage row format and the edge-based approach. A comparison between these storage schemes is performed, quantifying for most common linear elements the number of floating points operations, indirect addressing and memory requirements necessary to perform matrix–vector products. The overall performance of the preconditioned conjugate gradient method is measured for different situations involving 2D and 3D diffusion and elasticity problems, highlighting the pros and cons of each storage scheme.