# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# get departure points
xd_all = np.zeros(aap.N)
yd_all = np.zeros(aap.N)
# advect those in the annulus
c1, c2, c3 = AEP.get_categories()
c1n, c2n, c3n = AEP.get_category_Ns()
# category 1 and 2
c1_2 = np.logical_or(c1, c2)
c1_2n = c1n + c2n
uxh = ebdy.interpolate_to_points(ux, aap.x, aap.y)
uyh = ebdy.interpolate_to_points(uy, aap.x, aap.y)
vxh = ebdy.interpolate_to_points(vx, aap.x, aap.y)
vyh = ebdy.interpolate_to_points(vy, aap.x, aap.y)
uh = ebdy.interpolate_to_points(u, aap.x, aap.y)
vh = ebdy.interpolate_to_points(v, aap.x, aap.y)
SLM = np.zeros([
c1_2n,
] + [2, 2], dtype=float)
SLR = np.zeros([
c1_2n,
] + [
2,
], dtype=float)
SLM[:, 0, 0] = 1 + dt * uxh[c1_2]
SLM[:, 0, 1] = dt * uyh[c1_2]
# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# get departure points
xd_all = np.zeros(aap.N)
yd_all = np.zeros(aap.N)
# advect those in the annulus
c1, c2, c3 = AEP.get_categories()
c1n, c2n, c3n = AEP.get_category_Ns()
# category 1 and 2
c1_2 = np.logical_or(c1, c2)
c1_2n = c1n + c2n
uxh = ebdy.interpolate_to_points(ux, aap.x, aap.y)
uyh = ebdy.interpolate_to_points(uy, aap.x, aap.y)
vxh = ebdy.interpolate_to_points(vx, aap.x, aap.y)
vyh = ebdy.interpolate_to_points(vy, aap.x, aap.y)
uh = ebdy.interpolate_to_points(u, aap.x, aap.y)
vh = ebdy.interpolate_to_points(v, aap.x, aap.y)
SLM = np.zeros([
c1_2n,
] + [2, 2], dtype=float)
SLR = np.zeros([
c1_2n,
] + [
2,
], dtype=float)
SLM[:, 0, 0] = 1 + dt * uxh[c1_2]
SLM[:, 0, 1] = dt * uyh[c1_2]
# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# get departure points
xd_all = np.zeros(aap.N)
yd_all = np.zeros(aap.N)
# advect those in the annulus
c1, c2, c3 = AEP.get_categories()
c1n, c2n, c3n = AEP.get_category_Ns()
# category 1 and 2
c1_2 = np.logical_or(c1, c2)
c1_2n = c1n + c2n
uxh = ebdy.interpolate_to_points(ux, aap.x, aap.y)
uyh = ebdy.interpolate_to_points(uy, aap.x, aap.y)
vxh = ebdy.interpolate_to_points(vx, aap.x, aap.y)
vyh = ebdy.interpolate_to_points(vy, aap.x, aap.y)
uh = ebdy.interpolate_to_points(u, aap.x, aap.y)
vh = ebdy.interpolate_to_points(v, aap.x, aap.y)
SLM = np.zeros([
c1_2n,
] + [2, 2], dtype=float)
SLR = np.zeros([
c1_2n,
] + [
2,
], dtype=float)
SLM[:, 0, 0] = 1 + dt * uxh[c1_2]
SLM[:, 0, 1] = dt * uyh[c1_2]
(time.time() - st) * 1000))
st = time.time()
# now we need to interpolate onto things
AEP = ebdy.registered_partitions[ap_key]
GEP = ebdy.registered_partitions[gp_key]
# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# advect those in the annulus
# category 1
c1, c2, c3 = AEP.get_categories()
c1n, c2n, c3n = AEP.get_category_Ns()
uxh = ebdy.interpolate_to_points(ux, ap.x, ap.y)
uyh = ebdy.interpolate_to_points(uy, ap.x, ap.y)
vxh = ebdy.interpolate_to_points(vx, ap.x, ap.y)
vyh = ebdy.interpolate_to_points(vy, ap.x, ap.y)
uh = ebdy.interpolate_to_points(u, ap.x, ap.y)
vh = ebdy.interpolate_to_points(v, ap.x, ap.y)
SLM = np.zeros([
c1n,
] + [2, 2], dtype=float)
SLR = np.zeros([
c1n,
] + [
2,
], dtype=float)
SLM[:, 0, 0] = 1 + dt * uxh[c1]
SLM[:, 0, 1] = dt * uyh[c1]
# now solve for sd, rd
res = objective(s, r)
mres = np.hypot(res[:, 0], res[:, 1]).max()
tol = 1e-12
while mres > tol:
J = Jac(s, r)
d = np.linalg.solve(J, res)
s -= d[:, 0]
r -= d[:, 1]
res = objective(s, r)
mres = np.hypot(res[:, 0], res[:, 1]).max()
# get the departure points
xd = bx_interp(s) + nx_interp(s) * r
yd = by_interp(s) + ny_interp(s) * r
# now interpolate to c
ch3 = ebdy.interpolate_to_points(c - dt * scaled_nonlinearity(c), xd,
yd)
ch12 = ebdy.interpolate_to_points(ecnew, aap.x[c12], aap.y[c12])
# get the full thing
ch = np.empty(aap.N)
ch[c12] = ch12
ch[c3] = ch3
# set the grid values
c_new.grid_value[new_ebdyc.phys_not_in_annulus] = ch[:gp.N]
# set the radial values
c_new.radial_value_list[0][:] = ch[gp.N:].reshape(ebdy.radial_shape)
# overwrite under grid under annulus by radial grid
_ = new_ebdyc.interpolate_radial_to_grid(c_new.radial_value_list,
c_new.grid_value)
# save this for a moment
c_force = c_new.copy()