Classical time stepping with Irksome

Irksome generates Runge-Kutta methods for semi-discrete Firedrake UFL forms. It can provide the classical time integrator while Yonderdrake provides a spatial fractional operator:

import firedrake as fd
import irksome
from yonderdrake import SpectralFractionalLaplacian

mesh = fd.UnitSquareMesh(24, 24)
V = fd.FunctionSpace(mesh, "CG", 1)
u = fd.Function(V)
v = fd.TestFunction(V)
t = fd.Constant(0.0)
dt = fd.Constant(0.01)
bc = fd.DirichletBC(V, 0.0, "on_boundary")

F = (
    fd.inner(irksome.Dt(u), v)
    + fd.inner(
        SpectralFractionalLaplacian(u, 0.7, bcs=bc),
        v,
    )
) * fd.dx
stepper = irksome.TimeStepper(
    F,
    irksome.GaussLegendre(1),
    t,
    dt,
    u,
    bcs=bc,
    solver_parameters={
        "mat_type": "matfree",
        "snes_type": "ksponly",
        "ksp_type": "gmres",
    },
)
stepper.advance()

Irksome transforms Dt(u). The external operator supplies its action and derivative. Use a matrix-free Jacobian for this composition, as in the example above.

Irksome is optional and does not evolve fractional memory: it supplies the classical time integrator only. Use FractionalTimeStepper when the residual contains a fractional time marker. The Gallery shows both compositions.

See the Irksome repository for installation and its complete time-stepping interface.