3.1.1.3. c3po.couplers.CrossedSecantCoupler module

Contain the class CrossedSecantCoupler.

class c3po.couplers.CrossedSecantCoupler.CrossedSecantCoupler(physics, exchangers, dataManagers)

Bases: Coupler

CrossedSecantCoupler inherits from Coupler and proposes a fixed point algorithm with crossed secant acceleration.

The class proposes an algorithm for the resolution of \(F(X) = X\). Thus CrossedSecantCoupler 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 (the \(X\)).
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 CollaborativeDataManager.

At each iteration we do (with \(n\) the iteration number):

\[ \begin{align}\begin{aligned}X^{n+1} = F(X^{n}) - (F(X^{n}) - X^{n}).[(F(X^{n}) - F(X^{n-1})).(F(X^{n}) - X^{n} -\\(F(X^{n-1}) - X^{n-1}))]/(||F(X^{n}) - X^{n} - (F(X^{n-1}) - X^{n-1})||^2)\end{aligned}\end{align} \]

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

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

The default maximum number of iterations is 100. Call setConvergenceParameters() to change it.

__init__(physics, exchangers, dataManagers)

Build a CrossedSecantCoupler object.

Parameters:

physics (list[PhysicsDriver], list[Coupler]) – 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 \(||F(X^{n}) - X^{n}|| / ||X^{n+1}|| < \rm{tolerance}\).
maxiter – The maximal number of iterations.

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 the damped fixed-point algorithm.