Hi there,
currently I'am working on electric field simulation problems. I try to implement a solver that can handle large distances (1 mm) up to very small ones (0.1 nm).
I use the finite differences method to solve the Poisson Equation, because it's possible to easily calculate these problems on a GPU.
During the implementation I came across a mathematical problem, which is even difficult for me to define. With finite differences there are no corner radii but all corners are 'sharp' right angles. Since the numerical simulation has a limited resolution, the solver does not determine an infinitely high field at such a 'sharp' corner, but a finite value. My feeling is that there should be a mathematical connection between the resolution of my finite differences program and what I call a virtual corner radius. I would be very happy if I could set a curvature via the resolution of the simulation at the same time, but I need a clear mathematical connection for this.
I would be very grateful if someone could help me to sort out this problem. I hope I have asked the question in the right place, excuse me if not.
Thanks in advance
peterudo
currently I'am working on electric field simulation problems. I try to implement a solver that can handle large distances (1 mm) up to very small ones (0.1 nm).
I use the finite differences method to solve the Poisson Equation, because it's possible to easily calculate these problems on a GPU.
During the implementation I came across a mathematical problem, which is even difficult for me to define. With finite differences there are no corner radii but all corners are 'sharp' right angles. Since the numerical simulation has a limited resolution, the solver does not determine an infinitely high field at such a 'sharp' corner, but a finite value. My feeling is that there should be a mathematical connection between the resolution of my finite differences program and what I call a virtual corner radius. I would be very happy if I could set a curvature via the resolution of the simulation at the same time, but I need a clear mathematical connection for this.
I would be very grateful if someone could help me to sort out this problem. I hope I have asked the question in the right place, excuse me if not.
Thanks in advance
peterudo