GLIMDA

GLIMDA is a solver for nonlinear index-2 DAEs f(q’(t,x),x,t)=0.

Details about the implementation (FORTRAN) can be found in the PhD dissertation:

General Linear Methods for Integrated Circuit Design

Author: Steffen Voigtmann

Support

• State events (root funtions) : False
• Step events (completed step) : True
• Time events : True

Usage

Import the solver together with the correct problem:

from assimulo.solvers import GLIMDA
from assimulo.problem import Implicit_Problem

Define the problem, such as:

def res(t, y, yd): #Note that y and yd are 1-D numpy arrays.
    res = yd[0]-1.0
    return N.array([res]) #Note that the return must be numpy array, NOT a scalar.

y0  = [1.0]
yd0 = [1.0]
t0  = 1.0

Create a problem instance:

mod = Implicit_Problem(res, y0, yd0, t0)

Note

For complex problems, it is recommended to check the available examples and the documentation in the problem class, Implicit_Problem. It is also recommended to define your problem as a subclass of Implicit_Problem.

Warning

When subclassing from a problem class, the function for calculating the right-hand-side (for ODEs) must be named rhs and in the case with a residual function (for DAEs) it must be named res.

Create a solver instance:

sim = GLIMDA(mod)

Modify (optionally) the solver parameters.

Parameters:

• atol Defines the absolute tolerance(s) that is to be used by the solver.
• backward Specifies if the simulation is done in reverse time.
• clock_step Specifies if the elapsed time of an integrator step should be timed or not.
• display_progress This option actives output during the integration in terms of that the current integration is periodically printed to the stdout.
• inith This determines the initial step-size to be used in the integration.
• maxh Defines the maximal step-size that is to be used by the solver.
• maxord Maximum order to be used (1-3).
• maxretry Defines the maximum number of consecutive number of retries after a convergence failure.
• maxsteps The maximum number of steps allowed to be taken to reach the final time.
• minh Defines the minimum step-size that is to be used by the solver.
• minord Minimum order to be used (1-3).
• newt Maximum number of Newton iterations.
• num_threads This options specifies the number of threads to be used for those solvers that supports it.
• order Determines if GLIMDA should use a variable order method (0) or a fixed order method (1-3).
• report_continuously This options specifies if the solver should report the solution continuously after steps.
• rtol Defines the relative tolerance that is to be used by the solver.
• store_event_points This options specifies if the solver should save additional points at the events, \(t_e^-, t_e^+\).
• time_limit This option can be used to limit the time of an integration.
• verbosity This determines the level of the output.

Simulate the problem:

t, y, yd = GLIMDA.simulate(tfinal, ncp, ncp_list)

Information:

• GLIMDA.get_options() Returns the current solver options.
• GLIMDA.get_supports() Returns the functionality which the solver supports.
• GLIMDA.get_statistics() Returns the run-time statistics (if any).
• GLIMDA.get_event_data() Returns the event information (if any).
• GLIMDA.print_event_data() Prints the event information (if any).
• GLIMDA.print_statistics() Prints the run-time statistics for the problem.