Source code for implementations.problem_classes.polynomial_test_problem

import numpy as np

from pySDC.core.Problem import ptype
from pySDC.implementations.datatype_classes.mesh import mesh, imex_mesh




class polynomial_testequation(ptype):
    """
    Dummy problem for tests only! In particular, the `solve_system` function just returns the exact solution instead of
    solving an appropriate system. This class is indented to be used for tests of operations that are exact on polynomials.
    """

    dtype_u = mesh
    dtype_f = mesh

    def __init__(self, degree=1, seed=26266):
        """Initialization routine"""

        # invoke super init, passing number of dofs, dtype_u and dtype_f
        super().__init__(init=(1, None, np.dtype('float64')))

        self.rng = np.random.RandomState(seed=seed)
        self.poly = np.polynomial.Polynomial(self.rng.rand(degree))
        self._makeAttributeAndRegister('degree', 'seed', localVars=locals(), readOnly=True)



    def eval_f(self, u, t):
        """
        Derivative of the polynomial.

        Parameters
        ----------
        u : dtype_u
            Current values of the numerical solution.
        t : float
            Current time of the numerical solution is computed.

        Returns
        -------
        f : dtype_f
            The right-hand side of the problem.
        """

        f = self.dtype_f(self.init)
        f[:] = self.poly.deriv(m=1)(t)
        return f




    def solve_system(self, rhs, factor, u0, t):
        """
        Just return the exact solution...

        Parameters
        ----------
        rhs : dtype_f
            Right-hand side for the linear system.
        factor : float
            Abbrev. for the local stepsize (or any other factor required).
        u0 : dtype_u
            Initial guess for the iterative solver.
        t : float
            Current time (e.g. for time-dependent BCs).

        Returns
        -------
        me : dtype_u
            The solution as mesh.
        """

        return self.u_exact(t)




    def u_exact(self, t, **kwargs):
        """
        Evaluate the polynomial.

        Parameters
        ----------
        t : float
            Time of the exact solution.
        u_init : pySDC.problem.testequation0d.dtype_u
            Initial solution.
        t_init : float
            The initial time.

        Returns
        -------
        me : dtype_u
            The exact solution.
        """
        me = self.dtype_u(self.init)
        me[:] = self.poly(t)
        return me






class polynomial_testequation_IMEX(polynomial_testequation):
    """
    IMEX version of the polynomial test problem that assigns half the derivative to the implicit part and the other half to the explicit part.
    Keep in mind that you still cannot Really perform any solves.
    """

    dtype_f = imex_mesh



    def eval_f(self, u, t):
        """
        Derivative of the polynomial.

        Parameters
        ----------
        u : dtype_u
            Current values of the numerical solution.
        t : float
            Current time of the numerical solution is computed.

        Returns
        -------
        f : dtype_f
            The right-hand side of the problem.
        """

        f = self.dtype_f(self.init)
        derivative = self.poly.deriv(m=1)(t)
        f.impl[:] = derivative / 2
        f.expl[:] = derivative / 2
        return f