Parallel SDC (`parallel_sdc`)¶

class pypint.solvers.parallel_sdc.ParallelSdc(**kwargs)[source]¶

Bases: pypint.solvers.i_iterative_time_solver.IIterativeTimeSolver, pypint.solvers.i_parallel_solver.IParallelSolver

Spectral Deferred Corrections method for solving first order ODEs.

The Spectral Deferred Corrections (SDC) method is described in [Minion2003] (Equation 2.7)

Default Values:

ThresholdCheck

max_threshold: 10

min_threshold: 1e-7

conditions: ('residual', 'iterations')

num_time_steps: 1

num_nodes: 3

Given the total number of time steps \(T_{max}\), number of integration nodes per time step \(N\), current time step \(t \in [0,T_{max})\) and the next integration node to consider \(n \in [0, N)\). Let \([a,b]\) be the total time interval to integrate over. For \(T_{max}=3\) and \(N=4\), this can be visualized as:

   a                                            b
   |                                            |
   |    .    .    |    .    .    |    .    .    |
t  0    0    0    0    1    1    1    2    2    2
n  0    1    2    3    1    2    3    1    2    3
i  0    1    2    3    4    5    6    7    8    9

In general, the value at \(a\) (i.e. \(t=n=i=0\)) is the initial value.

See also

IIterativeTimeSolver :: implemented interface
IParallelSolver :: mixed-in interface

_adjust_interval_width()[source]¶: Adjust width of time interval

_init_new_interval(start)[source]¶

Initializes a new work interval

Parameters:	start (`float`) – start point of new interval
Returns:	has_work – `True` if new interval have been initialized; `False` if no new interval have been initialized (i.e. new interval end would exceed end of time given by problem)
Return type:	`bool`

_init_new_state()[source]¶

Initialize a new state for a work task

Usually, this starts a new work task. The previous state, if applicable, is stored in a stack.

init(problem, integrator, **kwargs)[source]¶

Initializes SDC solver with given problem and integrator.

Parameters:

num_time_steps (int) – Number of time steps to be used within the time interval of the problem.
num_nodes (int) – (otional) number of nodes per time step
nodes_type (INodes) – (optional) Type of integration nodes to be used (class name, NOT instance).
weights_type (IWeightFunction) – (optional) Integration weights function to be used (class name, NOT instance).
classic (bool) – (optional) Flag for specifying the type of the SDC sweep. True: (default) For the classic SDC as known from the literature; False: For the modified SDC as developed by Torbjörn Klatt.

Raises:

ValueError –

if given problem is not an IInitialValueProblem
if number of nodes per time step is not given; neither through num_nodes, nodes_type nor integrator

Returns:	number_of_nodes – Number of integration nodes used within one time step.
Return type:	`int`

Parallel SDC (parallel_sdc)¶

Parallel SDC (`parallel_sdc`)¶