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ExpInt

ExpInt contains tools to aid in the implementation of exponential integrators. A few algorithms, including the Exp4 algorithm (Hochbruck, Lubich, Selhofer) are implemented.

Quickstart

This is an example of how to call the Exp4_adaptive integrator. It uses an included formulation of a quadratic ODE.

Details can be found in expint.problems.QuadraticODE.

from expint.problems import QuadraticODE
from expint.methods import Exp4_adaptive
e4 = Exp4_adaptive(QuadraticODE(1))
t,y = e4.integrate(x0=1.0, t0=0.0, tend=0.9)
print "error:",abs(10-y[-1])

Documentation

A Sphinx documentation can be found at http://rngantner.github.com/ExpInt . Sources are in the doc/ directory.

Files

Description of the files in this directory:

  • Examples.py

    • Contains various differential equations (as specializations of the RHS class)
    • Loops over ODEs, Methods and N/tol values to create convergence plots, result plots, etc.

  • Exp4.py

    • Contains the implementation of the Exp4 algorithm.
    • Class Exp4: uses equidistant nodes; achieves order 4, but is often slow (no Krylov space adaptivity)
    • Class Exp4_adaptive: changes timestep size based on local error estimators and Krylov space error estimator

  • HeatEquation.py

    • Contains a spatial FE discretization of the heat equation as a subclass of the class RHS
    • Implements all necessary functions needed by Exp4; procedural Df(x)*u, g(u), ...
    • Internally stores a sparse LU decomposition to reduce computational cost.

  • KrylovPhi.py

    • Implements a helper class for the Exp4 algorithm that manages the Krylov space, provides error estimation and statistics.

  • MatrixExponential.py

    • Nice class structure for describing matrix exponentials; not used in Exp4 due to its highly specialized requirements.

  • Method.py

    • Base class "Method" from which all methods should derive.
    • A few methods are implemented here, including ExplicitEuler, ExpRosenbrockEuler, ode45 (wrapper), ...

  • Problem.py

    • "Problem" class which provides a link between RHSs and Methods.
    • Provides some convenience functions; can differentiate between adaptive and non-adaptive methods (if they derive from correct classes).

  • RHS.py

    • Base class for a general right-hand side.
    • One specialization, "DfRHS", describes ODE of the form u' = Df(u)*u+g(u), Df is the Jacobian of u'=f(u)

  • Timings.py

    • executes timings of variouse algorithms and problems

  • ode45.py

    • Implementation of the ode45 algorithm (inspired by MATLAB implementation; copied from "Numerik für Physiker" files and improved a bit.)