Jacobian Reform Time Stride#

Jacobian Reform Time Stride = <integer>

Description / Usage#

This optional card has a single input parameter:

<integer>: k, the stride length for Jacobian reformations ( \(k \geq 1\) ).

The Jacobian Reform Time Stride card is optional; there is no default.

Examples#

Three examples are provided to illustrate how to use this card.

Example #1:

Number of Newton Iterations = 12 1

Modified Newton Tolerance = 1.9 0.1

Jacobian Reform Time Stride = 2

Newton correction factor = 1

This will reform the Jacobian every 2 steps. Furthermore, if the convergence rate falls below 1.9 or the L₁ residual is greater than 0.1 on an off-stride step a Jacobian reformation will occur. Specifically, the*Modified Newton Tolerance* takes precedence over a reformation stride setting (from either Number of Newton Iterations or Jacobian Reform Time Stride).

Example #2:

Number of Newton Iterations = 12 1

# Modified Newton Tolerance = 1.9 0.1

Jacobian Reform Time Stride = 2

Newton correction factor = 1

Note this differs from the previous example only by omitting the Modified Newton Tolerance card. This causes the Jacobian to be reformed every other time step.

Example #3:

Number of Newton Iterations = 12 2

# Modified Newton Tolerance = 1.9 0.1

Jacobian Reform Time Stride = 1

Newton correction factor = 1

We’ve changed the Jacobian Reform Time Stride from 2 to 1 and changed the second parameter of the Number of Newton Iterations card from 1 to 2. This will cause the Jacobian to be reformed every other step.

Technical Discussion#

If the second parameter on the Number of Newton Iterations card is present and greater than 1, this Jacobian Reform Time Stride card is ignored. Otherwise, this card simply forces the Jacobian to be rebuilt every k Newton steps. Often, this card will allow you to speed up your runs by foregoing a fresh Jacobian formation, but still maintain strong convergence. Moreover, without a Jacobian formation, the lu solver (see the Solution Algorithm card) can use a previously factored matrix and simply do a resolve.