Coarse-Grid Correction

Problem

Apply a coarse-grid correction to the current fine-grid iterate x.

Solve the coarse problem e = A_coarse_inv * r_coarse for the error, prolong it with x_new = x + P*e, and return the corrected vector.

Hint

The correction removes the smooth part of the error that the fine smoother cannot fix.

case 1

in: [[1,1],[[1],[0]],[[0.5]],[2]]

expected: [2,1]

case 2

in: [[0,0,0],[[1],[0],[0]],[[2]],[1]]

expected: [2,0,0]

case 3

in: [[1,2],[[1,0],[0,1]],[[1,0],[0,0.5]],[1,2]]

expected: [2,3]

case 4

in: [[0,0],[[1],[1]],[[1]],[0]]

expected: [0,0]

Starter codePython

def coarse_grid_correction(x, P, A_coarse_inv, r_coarse):
    # Your code here
    pass

4 test cases · run your code against them in the editor