Eigenvalues of a Jacobian

Question

I have a function of the form dh/dt = f(h). I've implemented a UFL file to compute f and it's derivative with respect to h. Something like ...

scalar = FiniteElement("Lagrange", interval, 2)
phi = TestFunction(scalar)
f = Coefficient(scalar)
g = Coefficient(scalar)
h = Coefficient(scalar)

F = f*h.dx(0)*phi*dx + g*phi*dx
dh = TrialFunction(scalar)
J = derivative(F, h, dh)

I (analytically) compute the steady state solution h. I'd like to know the Eigenvalue of the Jacobian at h to assess the stability.

I then have C++ code that looks like

auto space = make_shared<RHS::FunctionSpace>(mesh);
auto J = make_shared<RHS::JacobianForm>(space, space);
J->h = h; J->f = f;

A = make_shared<dolfin::Matrix>();
dolfin::assemble(*A, *J);

Is there an easy way to compute the Eigenvalues of A?

Comments

this is from an old version of dolfin, but does the following help? https://fenicsproject.org/olddocs/dolfin/1.5.0/python/demo/documented/eigenvalue/python/documentation.html

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This is the same demo from the latest version of DOLFIN: https://fenicsproject.org/olddocs/dolfin/2016.2.0/python/demo/documented/eigenvalue/python/demo_eigenvalue.py.html.

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Thanks johannr.