Outer Product between two vectors to form a sparse matrix

General
1

Hi,

I want to assemble cross product of 2 vectors to the matrix. Here is the matrix;

D_{jk} = \int_{\Omega} \phi_i e^{i \omega \tau(\textbf{x})} d\textbf{x} \int_{\Omega} \frac{1}{\rho_0 (\chi)} \nabla{\phi_j} \cdot \textbf{n}_{ref} d\chi

When I try that, I am having ufl error;

  File "/home/ekrem/Dev/Venvs/dolfinx_v050/lib/python3.10/site-packages/ufl/constantvalue.py", line 437, in as_ufl
    raise UFLValueError("Invalid type conversion: %s can not be converted"
ufl.log.UFLValueError: Invalid type conversion: <dolfinx.fem.forms.Form object at 0x7f324e9b1710> can not be converted to any UFL type.

Here is my MWE;

from dolfinx.fem import Function, FunctionSpace, form
from ufl import Measure, TestFunction, TrialFunction, inner, as_vector, grad, exp, cross, dx
from dolfinx.mesh import create_unit_cube
from mpi4py import MPI
from dolfinx.fem.petsc import assemble_matrix

mesh = create_unit_cube(MPI.COMM_WORLD, 10, 10,10)

rho = 1.25

degree = 1
V = FunctionSpace(mesh, ("Lagrange", degree))
 
phi_i = TrialFunction(V)
phi_j = TestFunction(V)

omega = 10
tau = 0.001

n_ref = as_vector([0,0,1])
        
left_vector  = form( phi_i  *  exp(1j*omega*tau)  *  dx)
right_vector = form(inner(n_ref,grad(phi_j)) / rho  * dx)

total_form = cross(left_vector, right_vector)

D = assemble_matrix(total_form)
D.assemble()

How could I get my matrix assembled?

Thanks in advance.

2

What you are doing here is mixing compiled forms (i.e. C kernels for assembly) with ufl syntax.

The operation that you are trying to do, the outer product of two vectors is not trivial as far as Iā€™m aware, as it requires quite alot of communication to make a dense matrix. PETSc for instance does not recommend ever assembling this matrix: [petsc-users] vector outer product

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