Source code for laplace

import dolfin


def laplace() -> dolfin.Function:
    r"""Solve the Lapace equation

    .. math::

        \Delta u = 0

    with the following Dirichlet boundary conditions

    .. math::

        u(0, y, z) = 0 \\
        u(1, y, z) = 1

    Returns
    -------
    dolfin.Function
        Solution to the Laplace equation
    """
    mesh = dolfin.UnitCubeMesh(3, 3, 3)
    left = dolfin.CompiledSubDomain("x[0] <= DOLFIN_EPS")
    right = dolfin.CompiledSubDomain("x[0] >= 1 - DOLFIN_EPS")
    V = dolfin.FunctionSpace(mesh, "CG", 1)

    u = dolfin.TrialFunction(V)
    v = dolfin.TestFunction(V)
    a = dolfin.dot(dolfin.grad(u), dolfin.grad(v)) * dolfin.dx
    L = v * dolfin.Constant(0) * dolfin.dx

    t = dolfin.Function(V)

    left_bc = dolfin.DirichletBC(V, 0, left)
    right_bc = dolfin.DirichletBC(V, 1, right)
    bcs = [left_bc, right_bc]
    dolfin.solve(
        a == L,
        t,
        bcs,
    )
    return t


if __name__ == "__main__":  # pragma: nocover
    t = laplace()
    dolfin.File("t.pvd") << t