import multigrid
from ntiling import TilingBuilder
from drawing.pil_draw_simple import Draw
palette = [
"#7fb414",
"#fac70b",
"#127681",
"#df0e62",
"#21174a",
]
draw = Draw(scale=150, width=3 * 1280, height=3 * 1280, bg_color=palette[-1])
draw.line_color = None
index_range = (-2, 2)
grid = multigrid.Multigrid(9)
tiling_builder = TilingBuilder(grid)
tiling_builder.prepare_grid(index_range)
tiling_builder.generate_rhomb_list()
for rhomb in tiling_builder._rhombs.values():
col = (rhomb.type() in (4, 5, 3, 6, 2, 7)) + (rhomb.type() in (
3, 6, 2, 7)) + (rhomb.type() in (2, 7))
if col != 0:
new = []
for a, b in rhomb.get_edges():
new.append((a.get_xy(form="xy1") + b.get_xy(form="xy1")) / 2)
# coords = rhomb.center(form="xy")
draw.polygon(new, color=palette[col])
else:
draw.polygon(rhomb.xy(form="xy1"), color=palette[col])
# the analytic solution
return -np.sin(x) + x * np.sin(1.0)
def f(x):
# the righthand side
return np.sin(x)
# test the multigrid solver
nx = 128
# create the multigrid object
a = multigrid.Multigrid(nx,
bc_left_type="dirichlet",
bc_right_type="dirichlet",
verbose=1,
true_function=true)
# initialize the solution to 0
a.init_solution()
# initialize the RHS using the function f
a.init_rhs(f(a.x))
# solve to a relative tolerance of 1.e-11
elist, rlist = a.solve(rtol=1.e-11)
ncycle = np.arange(len(elist)) + 1
# get the solution
import multigrid
from ntiling import TilingBuilder
from drawing.pil_draw_simple import Draw
palette = [
"#293462",
"#216583",
"#00818a",
"#f7be16",
]
draw = Draw(scale=90, width=3 * 1280, height=3 * 1280, bg_color=palette[-2])
draw.line_color = None
index_range = (-1, 1)
grid = multigrid.Multigrid(23)
tiling_builder = TilingBuilder(grid)
tiling_builder.prepare_grid(index_range)
tiling_builder.generate_rhomb_list()
for rhomb in tiling_builder._rhombs.values():
for a, b in rhomb.get_edges():
draw.edge(a.get_xy(homogenous=False),
b.get_xy(homogenous=False),
color=palette[-1],
width=4)
draw.show()
import multigrid
from ntiling import TilingBuilder
from drawing.pil_draw_simple import Draw
palette = [
"#ffee7d",
"#b767ff",
"#44fadd",
"#ffe0f7",
"#fe91ca",
]
draw = Draw(scale=110, width=3 * 1280, height=3 * 1280, bg_color=palette[-2])
draw.line_color = None
index_range = (-3, 3)
grid = multigrid.Multigrid(17)
tiling_builder = TilingBuilder(grid)
tiling_builder.prepare_grid(index_range)
tiling_builder.generate_rhomb_list()
for rhomb in tiling_builder._rhombs.values():
new = []
for a, b in rhomb.get_edges():
new.append((a.get_xy() + b.get_xy()) / 2)
p1 = new[-1]
for p2 in new:
draw.edge(p2[:2], p1[:2], color=palette[-1], width=8)
p1 = p2
draw.show()
# palette = [
# "#7fb414",
# "#df0e62",
# "#127681",
# "#fac70b",
# "#092a35",
# ]
draw = Draw(scale=90, width=4 * 1280, height=4 * 1280, bg_color=palette[-1])
draw.line_color = None
index_range = (-4, 4)
offsets = list(
map(
float,
"0.04885131 0.38705046 0.15540683 0.37524718 0.09360688 0.04554864 0.0424169"
.split(" ")))
grid = multigrid.Multigrid(7, offsets)
# grid = multigrid.Multigrid(7, [0.11071195, 0.40178219, 0.38167641, 0.05840904, 0.26593674, 0.30876262, 0.40169052])
tiling_builder = TilingBuilder(grid)
tiling_builder.prepare_grid(index_range)
tiling_builder.generate_rhomb_list()
for rhomb in tiling_builder._rhombs.values():
c = (rhomb.type() in (1, 6, 2, 5)) + (rhomb.type() in (1, 6))
# c = (rhomb.type() in (1, 2, 5, 6)) + (rhomb.type() in (1, 6))
draw.polygon(rhomb.xy(), color=palette[c])
for a, b in rhomb.get_edges():
draw.edge(a.get_xy(homogenous=False),
b.get_xy(homogenous=False),
color=palette[-2],
width=6)