oblique_schmidt#

greensfield.algorithms.oblique_schmidt(phi, boundary, delta, shape, z_depth, l_hat)[source]#

Calculate scalar magnetic potential using the oblique Schmidt method [Sch64].

Note

This function is accelerated with numba.

Parameters:

  • phi (array-like) – Scalar magnetic potential as a function of \(x\), \(y\), and \(z\) with shape (n_x,n_y,n_z). This should be initially an empty array.

  • boundary (array-like) – Magnetic field in the \(z\)-direction at \(z=0\) as a function of \(x\) and \(y\) with shape (n_x,n_y).

  • delta (array-like) – Size of each grid cell in \(x\), \(y\), and \(z\) with shape (3,). Must have same units as z_depth.

  • shape (array-like) – Number of grid cells in \(x\), \(y\), and \(z\) with shape (3,).

  • z_depth (float) – The depth below the surface at which the magnetic monopole is submerged.

  • l_hat (array-like) – Unit vector with shape (3,) indicating the surface normal of the lower boundary of the computational domain.

Returns:

phi – Scalar magnetic potential as a function of \(x\), \(y\), and \(z\) with shape (n_x,n_y,n_z).

Return type:

array-like