ALTERNATING DIRECTION PRECONDITIONING FOR NONSYMMETRIC SYSTEMS OF LINEAR-EQUATIONS

Preconditioning strategies based on the application of the alternating direction implicit (ADI) method to large systems of linear equations of the form (H + V)u = f, where both H and V can be ''easily inverted,'' are presented and analyzed. Besides other applications, such systems arise naturally from finite difference discretizations of two-dimensional elliptic boundary value problems. The emphasis here is on the case where H and V are nonsymmetric. The use of alternating direction preconditioning is especially attractive for massively parallel computers since, during each iteration, a large number of tridiagonal systems must be solved simultaneously. Numerical experiments are presented comparing ADI with other preconditioners for some examples of discretized nonselfadjoint elliptic boundary value problems including nonseparable cases.