Residual Ratio Tolerance

Residual Ratio Tolerance = <float>

Description / Usage

This optional card sets the convergence criterion for the iterative solution of the linear matrix system solved at each Newton iteration. The input parameter is defined as

<float>

tol, a non-negative real number ( tol ≥ 0.0 ) specifying the value of the convergence criterion.

The default value of tol is 1.0e-6.

Examples

Following is a sample card:

Residual Ratio Tolerance = 1.0e-3

Technical Discussion

The value of tol is ignored when a direct factorization algorithm (such as lu) for the linear solve is specified in the Solution Algorithm card. When an iterative matrix solution technique is specified (such as gmres), tol acts as the inner iteration termination relative tolerance. Letting r₀ represent the initial residual norm, when the n_th iteration’s linear residual norm r_n satisfies r_n / r:sub :0 ≤ tol, the iterative solution is deemed acceptable and the inner iterations terminate. The number of iterations required is reported under the LIS column of the Newton iteration output. If the maximum number of iterations (specified in the Maximum Linear Solve Iterations card) is reached, then max appears instead of a number. Although the standard residual is usually used as the residual norm, the type of matrix residual norm used can be changed through the Matrix residual norm type card.