How to calculate an external force vector as the product of a stiffness matrix K and a prescribed vector u_p

Question

Hi, again.

As known, the external force vector can be obtained from the following codes:

dU_ext = dot(load, u_test)*ds(1) # reference external energy functional due to external load imposed on the boundary ds(1)
f_ext = assemble(dU_ext) # assembled external forces

Now, I want to calculate a similar external force vector as the product of a stiffness matrix K and a vector u_p containing prescribed displacements.

K = assemble(a) # stiffness matrix
bc.apply(u_p.vector()) # u_p contains the prescribed displacements

# the reference external forces
f_ext = inner(K, u_p) # does not work
f_ext = numpy.matmul(K.array(), u_p.vector.array()) # works, but yields an array rather than a Vector as the external forces given above

I want to arrive at an external force vector f_ext of the same type obtained by assemble().
Can someone give me any idea? Thank you!

Answer 1

I guess that you are looking for something similar to K*u_p.vector(). See the minimal example below

from dolfin import *

MyMesh = UnitSquareMesh(3,3)
imposed_displacement = Constant(1)

V = FunctionSpace(MyMesh, "Lagrange", 1)
u_p = Function(V)

u = TrialFunction(V)
v = TestFunction(V)
K = assemble(inner(grad(u), grad(v))*dx)
f = K*u_p.vector()

print type(f)

# Now, if you wish, you can use f as right-hand side of a linear system
solution = Function(V)
solve(K, solution.vector(), f)

Comments

Yes, Dr. Ballarin. Any better idea?

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I modified the answer to show you an example.

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Thanks a lot, Dr. Ballarin. I cannot imagine that it is so simple.
You really helped me!

Answer 2

It seems that the following codes work:

f_ext = Vector(N)
f_ext[:] = numpy.matmul(K.array(), u_p.vector.array())

Am I right?