Elliptic Grid Solvers

After performing a transfinite interpolation on a 2D contour we may wish to refine the generated solution. We can do so via an elliptic grid solver.

# settting things up

import numpy as np
import pymethods as pma
from pymethods.algorithms.transfinite_interpolation import Transfinite2d
from pymethods import pyplot as plt
import scipy
from pymethods.algorithms import elliptic_mesh_generation
import pathlib as pt

cwd = pt.Path(__file__).parent

dataset_folder = cwd/'../../Datasets/artery_structure_grid'
data_file = dataset_folder/'00000.npz'
data = np.load(data_file)
oct_pts = data["points"]

inner = np.s_[1:-1]
ip1 = np.s_[2:]
im1 = np.s_[0:-2]

# apply a for loop for the desired contours within the contour stack
for contour_id in [10, ]:
   ...

Let us load a contour and transfinitely interpolate with Transfinite2d

oct_contour = pma.arrays.Contour(
         oct_pts[:, :, contour_id]
      )

# as the method is 2-dimensional we will retain the basis and
# the centroid of the contour to flatten the grid
centroid = oct_contour.centroid
basis = oct_contour.calc_basis()

transfinite_interpolator = Transfinite2d(
   oct_contour
)

# the total number of points along each segment used for interpolation
N = 30

grid, (zeta_orig, eta_orig) = transfinite_interpolator.pts_mesh_uniform(
   N, N, return_params=True)