Orthogonalization

Orthogonalization = {classic | modified}

Description / Usage

This optional card selects the orthogonalization scheme used internally for the gmres solution algorithm (see the Solution Algorithm card). Valid options are

classic | classical

Two steps of classical Gram-Schmidt orthogonalization.

modified

A modified Gram-Schmidt orthogonalization.

If the Orthogonalization card is omitted, then the default selection is classic. Goma’s parser will accept classical as equivalent to classic.

Examples

Following is a sample card:

Orthogonalization = modified

Technical Discussion

By specifying modified, the user is greatly speeding up the gmres algorithm at the expense of possibly losing convergence. A good indication that you should not have used the modified setting is a premature “leveling off” of the sequence of residuals produced internally within gmres.