Calculating an overlap integral

1

Hello,

I am looking to find the correct method to calculate an integral over a 2D mesh defined as
\int_\Omega u_1(x,y)e^{iqx} u_2(x,y) dx dy
where q is a constant, u_1, u_2 are functions over the mesh.

Here is attempt 1 (for q = 1):

f = Expression('cos(x[0])', degree = 1)
integral_real = assemble(u1*f*u2*dx)
g = Expression('sin(x[0])', degree = 1)
integral_imag = assemble(u1*g*u2*dx)
print(integral_real + 1j*integral_imag)

Is this the right way to calculate such an integral?

2

Here you assume that u1 and u2 are real numbers, and the multiplication makes sense. However, if u1 and u2 are supposed to be complex you Need a further decomposition of u1 and u2 into its real and imaginary part.

As a side note, in dolfinx, there is support for complex numbers. You can test it in docker by using the image dolfinx/complex. The source code of dolfinx can be found here.

1 Like