Parameter choices for ADI-like methods on parallel computers (Q1286920)

A transpose free alternating direction implicit (ADI)-like method is developed. Classical ADI and some classical properties of the Gauss-Seidel method are briefly reviewed. Then, the new ADI-like iteration with tridiagonal solvers for one half step replaced by \(k\) Gauss-Seidel sweeps is defined and analyzed. This approximation method, which is trivially parallelized, is denoted as ADG\((\rho, k)\). \(\rho\) is the ADI parameter, which is considered also as multiple \(\rho\) case, and \(k\) is the number of Gauss-Seidel iterations used to approximate the tridiagonal solver. It is shown that the ADI-like iteration does not require parallel tridiagonal solvers in any direction. The convergence of the iteration is proven for a set of acceleration parameters associated with ADI. Moreover, it has almost no communication when a small number of iterations is used. Numerical experiments on a network of workstations and parallel computers are supplied.