The preconditioned simultaneous displacement method (PSD method) for elliptic difference equations

✍ Scribed by D.J. Evans; N.M. Missirlis

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 670 KB
• Volume: 22
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(80)90053-1

✦ Synopsis

This paper introduces the Preconditioned Simultaneous DispZacement iterative method (PSD method) in a new '%omputablel' form for the numerical solution of linear systems of the form AI.&, where the matrirc A is large and sparse. The convergence properties of the method are analysed under certain asswnptions on the matrix A. Moreover, "good" values (near the optimwni for the involved parameters are determined in terms of bounds on the eigenvalues of certain matrices.

Bounds on the reciprocal rate of convergence of the PSD method are aLso given. The method is shown to be superior over the well known Symmetric Successive Overrelaxation method (SSOR method) (at the optimum stage PSD is shozsn to converge approzimately two times faster than SSOR) and in certain cases over the Successive Overrelaxation wethod (SOR method).