def jump_condition(x,y,u):
u_desired = desired_func(x,y)
u_n_desired = hf.norm_grad(u_desired,(x,y),lvl_func)
#for Robin boundary condition only
def sigma(x,y):
return -0.25 * (hf.XYtoR(x-x0, y-y0)+10**-17)
sigma_Robin = sigma(x, y)
g_Robin = u_desired + sigma_Robin * u_n_desired
#################################
if(bnd_type == "Dirichlet"):
a_mesh = - u_desired
b_mesh = - beta_m * hf.grad_frame(u,(x,y),lvl_func)
elif(bnd_type == "Neumann"):
a_mesh = - u
b_mesh = - beta_m * u_n_desired
elif(bnd_type == "Robin_u"):
a_mesh = - u
b_mesh = - beta_m * (g_Robin - u)/sigma_Robin
elif(bnd_type == "Robin_u_n"):
a_mesh = -(g_Robin - sigma_Robin*u_n_desired)
b_mesh = - beta_m * hf.grad_frame(u,(x,y),lvl_func)
elif(bnd_type == "exact"):
a_mesh = - u_desired
b_mesh = - beta_m * u_n_desired
else:
raise Exception("error: invalid boundary format")
return (a_mesh, b_mesh)
global jmp_func
jmp_func = jump_condition
if (__name__ == "__main__"):
##generate poisson solver
plt.close("all")
initialize("u_n")
u_cur_result = sol_func(xmesh, ymesh)
for i in range(4):
initialize("u_n")
u_result = ps.poisson_jacobi_solver(u_cur_result, 200000,
(xmesh, ymesh), (beta_p, beta_m),
rhs_func, lvl_func, jmp_func)
u_n_result = hf.grad_frame(u_result, (xmesh, ymesh), lvl_func)
# plt.matshow(u_n_result)
# plt.colorbar()
fig_label = i
hf.plot3d_all(u_result, (xmesh, ymesh), sol_func, fig_label,
[True, True, True, True])
u_cur_result = u_result
# initialize()
# u_result2 = poisson_jacobi_solver(u_result1, 100000, (xmesh,ymesh), (beta_p, beta_m),rhs_func, lvl_func, jmp_func)
# u_n_result2 = grad_frame(u_result2, (xmesh, ymesh), lvl_func)
# plt.matshow(u_n_result2)
# plt.colorbar()
# plot3d_all(u_result2, (xmesh, ymesh), sol_func,[False, False,False,True])
# b_mesh = -beta_m * u_n[:,:]
# a_mesh = -(get_u_from_un(u_n, xmesh, ymesh))
## formulism 2
global jmp_func
jmp_func = jump_condition
######################################################################
if (__name__ == "__main__"):
##generate poisson solver
plt.close("all")
setup_grid(101)
u_cur_result = u_init
for i in range(10):
setup_equations("Dirichlet")
u_result = ps.poisson_jacobi_solver(u_cur_result, 200000,
(xmesh, ymesh), (beta_p, beta_m),
rhs_func, lvl_func, jmp_func)
u_n_result = hf.grad_frame(u_result, (xmesh, ymesh), lvl_func)
# plt.matshow(u_n_result)
# plt.colorbar()
fig_label = i
hf.plot3d_all(u_result, (xmesh, ymesh), sol_func, fig_label,
[False, False, False, True])
hf.print_error(u_result, (xmesh, ymesh), sol_func)
u_cur_result = u_result
u_n_result = hf.grad_frame(u_result, (xmesh, ymesh), lvl_func)
u_n_anal = hf.grad_frame(sol_func(xmesh, ymesh), (xmesh, ymesh),
lvl_func)
plt.matshow(u_n_result - u_n_anal)
print(hf.L_n_norm(np.abs(u_n_result - u_n_anal), 2))
# initialize()
# u_result2 = poisson_jacobi_solver(u_result1, 100000, (xmesh,ymesh), (beta_p, beta_m),rhs_func, lvl_func, jmp_func)
# u_n_result2 = grad_frame(u_result2, (xmesh, ymesh), lvl_func)