Stationary and Non­Stationary Preconditioned Iterative Schemes for the Solution of Elliptic Collocation Systems
by
Emmanuel Mathioudakis
Department of Sciences, Technical University of Crete, Chania 73100, Greece
Coauthors: E.P. Papadopoulou, Y.G. Saridakis

Abstract In this work we study the performance of three well known non­stationary or Krylov subspace methods, namely Orthomin, GMRES(m) and BiCG Stabilized, as they pertain to the solution of the Jacobi, SGS and SSOR preconditioned Collocation equations derived from the discretization of the Dirichlet model problem. It is shown that BiCGSTAB method performs substantialy better than GMRES(m) and Orthomin, while the best performance is achived with the SSOR precondition scheme. The later compared with the optimal SOR stationary scheme is found to be comparable, given that the value of the ! opt parameter is known. The Rich value analysis supports the performance analysis results. Keywords : Collocation, Orthomin, GMRES(m), BiCGSTAB, Jacobi, , SGS, SSOR, SOR, Rich Values.

Date received: January 15, 2001