Numerical algorithm and implementation
Iterative solution. Initial guess is just ?=0. Equation is regularized for stability:
- Use pseudospectral method
- Evaluate Laplacian implicitly (decouples in Fourier space)
- Evaluate nonlinear term explicitly in real space using 2 FFT’s.
- Boundary conditions inherently periodic on a square box - but we can be creative and still impose two fundamentally different BC’s
- Circular perfect conductor
- Perfect conductor matching the magnetic surfaces (elliptical)