Fixed_SLP,
on_surface=True,
form_b2c=False,
vector=True)
qfs_list.append(qfs)
sigmal = [qfs([
tau,
]) for qfs, tau in zip(qfs_list, taul)]
sigmav = np.column_stack([v2f(sigma) for sigma in sigmal])
out = Stokes_Layer_Apply(ebdyc.bdy_inward_sources,
ebdyc.grid_and_radial_pts,
forces=sigmav)
outu, outv = v2f(out)
gslpu, rslplu = ebdyc.divide_grid_and_radial(outu)
gslpv, rslplv = ebdyc.divide_grid_and_radial(outv)
uc[ebdyc.phys] += gslpu
vc[ebdyc.phys] += gslpv
for ur, rslp in zip(urs, rslplu):
ur += rslp
for vr, rslp in zip(vrs, rslplv):
vr += rslp
if plot:
mue = np.ma.array(uc, mask=ebdyc.ext)
fig, ax = plt.subplots()
clf = ax.pcolormesh(grid.xg, grid.yg, mue)
for ebdy in ebdys:
ax.plot(ebdy.bdy.x, ebdy.bdy.y, color='black', linewidth=3)
bv = solver.get_boundary_values(uers)
tau = np.linalg.solve(A, bcs2v - bv)
qfs = QFS_Evaluator(ebdy.bdy_qfs,
True, [
Singular_DLP,
],
Naive_SLP,
on_surface=True,
form_b2c=False)
sigma = qfs([
tau,
])
out = Laplace_Layer_Apply(ebdyc.bdy_inward_sources,
ebdyc.grid_and_radial_pts,
charge=sigma)
gslp, rslpl = ebdyc.divide_grid_and_radial(out)
rslp = rslpl[0]
uer += rslp.reshape(uer.shape)
ue[ebdyc.phys] += gslp
if plot:
fig, ax = plt.subplots()
ax.pcolormesh(grid.xg, grid.yg, mue)
ax.plot(ebdy.bdy.x, ebdy.bdy.y, color='black', linewidth=3)
ax.plot(ebdy.interface.x, ebdy.interface.y, color='white', linewidth=3)
# compute the error
rerr = np.abs(uer - uar)
gerr = np.abs(ue - ua)
gerrp = gerr[ebdyc.phys]
mgerr = np.ma.array(gerr, mask=ebdyc.ext)
# 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) # now solve diffusion equation if nu > 0: solver1 = ModifiedHelmholtzSolver(new_ebdyc, solver_type=solver_type, k=first_helmholtz_k) c_new_update = solver1(c_new/first_zeta, tol=1e-12, verbose=True) A = s1_singular(new_ebdyc.ebdys[0].bdy) - half_eye(new_ebdyc.ebdys[0].bdy) bvn = solver1.get_boundary_normal_derivatives(c_new_update.radial_value_list) tau = -np.linalg.solve(A, -bvn) qfs = QFS_Evaluator(new_ebdyc.ebdys[0].bdy_qfs, True, [Singular_SLP1,], Naive_SLP1, on_surface=True, form_b2c=False) sigma = qfs([tau,]) out = MH_Layer_Apply(new_ebdyc.bdy_inward_sources, new_ebdyc.grid_and_radial_pts, charge=sigma, k=first_helmholtz_k) gslp, rslpl = new_ebdyc.divide_grid_and_radial(out) rslp = rslpl[0] c_new_update.radial_value_list[0] += rslp.reshape(M, nb) c_new_update.grid_value[new_ebdyc.phys] += gslp c_new = c_new_update # overwrite under grid under annulus by radial grid _ = new_ebdyc.interpolate_radial_to_grid(c_new.radial_value_list, c_new.grid_value) else: # the second order method bx = ebdy.bdy.x + 0.5*dt*(3*ub - ubo_new_parm) by = ebdy.bdy.y + 0.5*dt*(3*vb - vbo_new_parm) bx, by, new_t = arc_length_parameterize(bx, by, return_t=True) bu_interp = interp1d(0, 2*np.pi, bdy.dt, ub, p=True) bv_interp = interp1d(0, 2*np.pi, bdy.dt, vb, p=True)