I am looking at a research paper that mentions integral operators (which in this case is brought up in reference to shading equations that are integral operators) and it says that we can create a matrix representation of integral operators using Galerkin projections. I am having difficulty finding specific literature on Galerkin projections. When I speak of integral operators $\textbf{K}$ of the form: $$g(y) = K f |_{y} = \int_X k(x,y)f(x)dx$$ where $k(x,y): X\times X\rightarrow \mathbb{R}$ is the kernel of the integral operator. Thanks for any help!
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
The idea of the Galerkin method is similar for partial differential equations and for integral equations, hence, any book on numerics of PDEs (that does finite elements) should be a good reference, and also every book on numerical methods for integral equations, e.g.
- "Integral Equations: Theory and Numerical Treatment" by Hackbusch or
- "Computational Methods for Integral Equations" by Delves and Mohamed.
There is also the original article "The discrete Galerkin method for integral equations" by Atkinson and Bogomolny
