An iterative method for the Helmholtz equation

Alvin Bayliss*, Charles I. Goldstein, Eli Turkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Original languageEnglish
Pages (from-to)443-457
Number of pages15
JournalJournal of Computational Physics
Issue number3
StatePublished - Mar 1983


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