Evaluating the LCD algorithm for solving linear systems of equations arising from implicit SUPG formulation of compressible flows

In this work we evaluate the performance of the left conjugate direction method recently introduced by Yuan, Golub, Plemmons and Cecílio for the solution of non-symmetric systems of linear equations arising from the implicit semi-discrete SUPG finite element formulation of advective–diffusive and inviscid compressible flows. We extend the original algorithm to accommodate restarts and typical element-by-element preconditioners. We also show how to select the first left conjugate vector to start LCD. Several problems are solved, accessing performance parameters such as number of iterations, memory requirements and CPU times, and results are compared with other algorithms, such as GMRES, TFQMR and Bi-CGSTAB