Solving Laplace equation iteratively

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Agata Bratek 2021-4-17

编辑： Agata Bratek 2021-4-17

Hi,

I was given a task to solve Laplace equation for electrostatic potential (a 2D approximation, so without z component).

After some mathematical transormations it looks like this:

where U is represented by a given matrix:

I am supposed to solve this iteratively along this equation:

while setting boundary conditions in each step imposed by the presence of conductors with a fixed potential.

I know only basic calculation in Matlab, and never worked with such complex equation before. I know I'm asking a lot, but can anyone help me?

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