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:

Information: