3.1.1.2. c3po.couplers.AndersonCoupler module

Contain the class AndersonCoupler.

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

Bases: Coupler

AndersonCoupler inherits from Coupler and proposes a fixed point algorithm with Anderson acceleration.

A QR decomposition is used for the optimization problem.

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

The first two iterations just do (with \(n\) the iteration number):

\[X^{n+1} = F(X^{n})\]

Then the Anderson acceleration starts and computes \(X^{n+1}\) as a linear combination of \([\alpha.F(X^{n-i}) + (1. - \alpha).X^{n-i}]\).

\(\alpha\), the relative fraction of \(F(X^{n-i})\) and \(X^{n-i}\) can be set with setAndersonDampingFactor(). Default value is 1 (only \(F(X^{n-i})\)).

The default order (number of previous states considered) is 2. Call setOrder() to change it.

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 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 AndersonCoupler 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().

setAndersonDampingFactor(andersonDampingFactor)

Set the damping factor of the method, the relative contribution of \(F(X^{k})\) and \(X^{k}\) on the calculation of next step.

Parameters:

andersonDampingFactor – The damping factor \(\alpha\) in the formula \(\alpha.F(X^{n-i}) + (1. - \alpha).X^{n-i}\).

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.

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.

setOrder(order)

Set the order of the method.

Parameters:

order – Order of Anderson method. This is also the number of previous states stored by the algorithm.

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 fixed point algorithm with Anderson acceleration.

Inspire de Homer Walker (walker@wpi.edu), 10/14/2011.

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

c3po.couplers.AndersonCoupler.deleteQRColumn(matrixQ, matrixR, dataTemp)

INTERNAL

Return type:

A new QR decomposition after deletion of one column.