human
Give me a the Python program you requested given the following:
3. Affine decomposition
For this problem the affine decomposition is straightforward:
$$m(u,v;\boldsymbol{\mu})=\underbrace{1}{\Theta^{m}_0(\boldsymbol{\mu})}\underbrace{\int{\Omega}uv \ d\boldsymbol{x}}{m_0(u,v)},$$
$$a(u,v;\boldsymbol{\mu})=\underbrace{\mu_0}{\Theta^{a}0(\boldsymbol{\mu})}\underbrace{\int{\Omega_1}\nabla u \cdot \nabla v \ d\boldsymbol{x}}{a_0(u,v)} \ + \  \underbrace{1}{\Theta^{a}1(\boldsymbol{\mu})}\underbrace{\int{\Omega_2}\nabla u \cdot \nabla v \ d\boldsymbol{x}}{a_1(u,v)},$$
$$f(v.
\boldsymbol{\mu}) = \underbrace{\mu_1}{\Theta^{f}0(\boldsymbol{\mu})} \underbrace{\int{\Gamma_{base}}v \ ds}{f_0(v)}.$$
We will implement the numerical discretization of the problem in the class
class UnsteadyThermalBlock(ParabolicCoerciveProblem):
by specifying the coefficients $\Theta^{m}(\boldsymbol{\mu})$, $\Theta^{a}_(\boldsymbol{\mu})$ and $\Theta^{f}(\boldsymbol{\mu})$ in the method
def compute_theta(self, term):
and the bilinear forms $m_(u, v)$, $a(u, v)$ and linear forms $f_(v)$ in
def assemble_operator(self, term):
assistant
#Here is the Python program you requested.
class UnsteadyThermalBlock(ParabolicCoerciveProblem):

    # Default initialization of members
    def __init__(self, V, **kwargs):
        # Call the standard initialization
        ParabolicCoerciveProblem.__init__(self, V, **kwargs)
        # ... and also store FEniCS data structures for assembly
        assert "subdomains" in kwargs
        assert "boundaries" in kwargs
        self.subdomains, self.boundaries = kwargs["subdomains"], kwargs["boundaries"]
        self.u = TrialFunction(V)
        self.v = TestFunction(V)
        self.dx = Measure("dx")(subdomain_data=self.subdomains)
        self.ds = Measure("ds")(subdomain_data=self.boundaries)

    # Return custom problem name
    def name(self):
        return "UnsteadyThermalBlock1RB"

    # Return the alpha_lower bound.
    def get_stability_factor_lower_bound(self):
        return min(self.compute_theta("a"))

    # Return theta multiplicative terms of the affine expansion of the problem.
    def compute_theta(self, term):
        mu = self.mu
        if term == "m":
            theta_m0 = 1.
            return (theta_m0, )
        elif term == "a":
            theta_a0 = mu[0]
            theta_a1 = 1.
            return (theta_a0, theta_a1)
        elif term == "f":
            theta_f0 = mu[1]
            return (theta_f0,)
        else:
            raise ValueError("Invalid term for compute_theta().")

    # Return forms resulting from the discretization of the affine expansion of the problem operators.
    def assemble_operator(self, term):
        v = self.v
        dx = self.dx
        if term == "m":
            u = self.u
            m0 = u * v * dx
            return (m0, )
        elif term == "a":
            u = self.u
            a0 = inner(grad(u), grad(v)) * dx(1)
            a1 = inner(grad(u), grad(v)) * dx(2)
            return (a0, a1)
        elif term == "f":
            ds = self.ds
            f0 = v * ds(1)
            return (f0,)
        elif term == "dirichlet_bc":
            bc0 = [DirichletBC(self.V, Constant(0.0),...