Efficient scaling algorithms for projection solvers in the finite element solution to coupled consolidation

To improve conditioning of matrices arising from the FE solution to Biot's consolidation equations, we investigate a number of scaling algorithms, inclucting simple diagonal scaling, modified scaling by the selection of appropriate non-diagonal factors, and a scaling minimizing the sum of the squares of the logarithms of the matrix entries. Results from 2D and 3D large size examples show that preliminary scaling may play a basic role in accelerating the convergence of projection solvers such as Bi-CGSTAB and TFQMR.