On 7/12/19 11:28 AM, 'Maxi Miller' via deal.II User Group wrote:
> It is difficult to write it as a single integral. The operation is similar to
> the split-step fourier method, i.e. transforming the column vector f(r) once
> using
> g(rho)=2\pi\int_0^\infty rf(r)J_0(2\pi\rho r)dr,
> multiplying it with a vector, and transforming it back using
> f(r) = 2\pi\int_0^\infty\rho g(\rho)J_0(2\pi\rho r)d\rho
> The operation is for radially symmetric systems, i.e. with z along the
> x-axis,
> and r along the y-axis. When starting on the left border with f_0, i.e. at
> position z = 0, doing the operation mentioned above gives the values for the
> nodes at z = 1, when enumerating the nodes from 0 to n along the z axis, and
> having equidistant nodes along the z-axis. Those integrals can be replaced by
> a matrix-vector-multiplication, thus making it easier to implement
> numerically.
This makes sense -- every linear operator can be represented as a matrix. So
yes, you can express the operation as a matrix, and of course you can express
this matrix using the deal.II classes.
But I'm not clear what your question is then. Are you asking how to build this
matrix?
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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