Hi,
I apologize for this question, but I wanted to make sure I understand how to solve a simple eigenvalue equation over a 2D mesh using NGSolve. The goal is to get eigenvalues and eigenvectors at each point of the mesh, with the intention of doing more post-processing later. Let's say I have some generally complex-valued 2x2 matrix $A(x,y)$, and I simply want to calculate $V$ and $\lambda$ in the eigenvalue equation: $A V = \lambda V$. If $A$ is Hermitian, $\lambda$ are real, and $V$ are generally complex-valued.
Since there's no FEM yet, I could easily do this using NumPy's linalg(), but I want to see how it can be done using NGSolve. I would want to calculate each $V(x,y)$ and $\lambda(x,y)$ and plot the latter over the mesh. Ultimately, I will be taking derivatives of $V$ and taking dot products, but I want to get this first step down.
Is there a minimal example I could use for reference? I saw some articles and posts about PINVIT, but I want to make sure I am not over-complicating things.
Thank you!
