3.1.1.6. c3po.couplers.JFNKCoupler module

Contain the class JFNKCoupler.

class c3po.couplers.JFNKCoupler.JFNKCoupler(physics, exchangers, dataManagers)

Bases: Coupler

JFNKCoupler inherits from Coupler and proposes a Jacobian-Free Newton Krylov coupling algorithm.

This is a Newton algorithm using a Krylov (GMRES) method for the linear system solving.

The Jacobian matrix is not computed, but the product of the jacobian matrix with a vector \(v\) is approximated by a Taylor formula (\(J_u\) is the jacobian of \(F\) at the point \(u\)):

\[J_u v \approx (F(u + \varepsilon v) - F(u))/\varepsilon\]

\(\varepsilon\) is a parameter of the algorithm. Its default value is 1E-4. Call setEpsilon() to change it

JFNKCoupler is a Coupler working with :

• A single PhysicsDriver (possibly a Coupler) defining the calculations to be made each time \(F\) is called.

• A list of DataManager allowing to manipulate the data in the coupling.

• Two Exchanger allowing to go from the PhysicsDriver to the DataManager and vice versa.

Each DataManager is normalized with its own norm got after the first iteration. They are then used as a single DataManager| using :class:.CollaborativeDataManager`.

As the Newton algorithm solves for \(F(X) = 0\), in order to be coherent with the fixed point coupling algorithms, \(F(x)\) is defined as \(F(X) = f(X) - X\), where \(f\) is the output of the physicsDriver.

The convergence criteria is : \(||f(X^{n}) - X^{n}|| / ||f(X^{n})|| < \rm{tolerance}\). The default norm used is the infinite norm. Coupler.setNormChoice() allows to choose another one.

The default Newton tolerance is 1.E-6. Call setConvergenceParameters() to change it.

The default maximum Newton number of iterations is 10. Call setConvergenceParameters() to change it.

The default Krylov tolerance is 1.E-4. Call setKrylovConvergenceParameters() to change it.

The default maximum Krylov iteration is 100. Call setKrylovConvergenceParameters() to change it.

__init__(physics, exchangers, dataManagers)

Build a JFNKCoupler object.

Parameters:

• physics (list[PhysicsDriver]) – List of only one PhysicsDriver (possibly a Coupler).

• exchangers (list[Exchanger]) – List of exactly two Exchanger allowing to go from the PhysicsDriver to the DataManager and vice versa.

• dataManagers (list[DataManager]) – List of DataManager.

getSolveStatus()

See PhysicsDriver.getSolveStatus().

setConvergenceParameters(tolerance, maxiter)

Set the convergence parameters (tolerance and maximum number of iterations).

Parameters:

• tolerance – The convergence threshold in \(||f(X^{n}) - X^{n}|| / ||f(X^{n})|| < \rm{tolerance}\).

• maxiter – The maximal number of iterations.

setEpsilon(epsilon)

Set the epsilon value of the method.

Parameters:

epsilon – The epsilon value in the formula \(J_u v \approx (F(u + \varepsilon v) - F(u))/\varepsilon\).

setFailureManagement(leaveIfSolvingFailed)

Set if iterations should continue or not in case of solver failure (solveTimeStep() returns False).

Parameters:

leaveIfSolvingFailed (bool) – Set False to continue the iterations, True to stop. Default: False.

setKrylovConvergenceParameters(tolerance, maxiter)

Set the convergence parameters (tolerance and maximum number of iterations) of the Krylov method.

Parameters:

• tolerance – The convergence threshold of the Krylov method.

• maxiter – The maximal number of iterations of the Krylov method.

setPrintLevel(level)

Set the print level during iterations (0=None, 1 keeps last iteration, 2 prints every iteration).

Parameters:

level (int) – Integer in range [0;2]. Default: 2.

solveTimeStep()

Solve a time step using Jacobian-Free Newton Krylov algorithm.

See also c3po.PhysicsDriver.PhysicsDriver.solveTimeStep().

c3po.couplers.JFNKCoupler.solveTriang(matrixA, vectorB)

INTERNAL.

Solves a triangular linear system.