def rk3(phi, exact_phi, temp_phi, deri, Hhat, dt):
temp_phi.assign(phi)
#compute u1, stored in var_list
bdry_values = bdry.get_bdry_values(exact_phi)
hdw.get_deri(deri[0], phi, bdry_values, 0, "+")
hdw.get_deri(deri[1], phi, bdry_values, 0, "-")
u1_form = phi - dt*Hhat
project(u1_form, phi.function_space(), function=phi)
#compute u2, stored in var_list
bdry_values = bdry.get_bdry_values(exact_phi)
hdw.get_deri(deri[0], phi, bdry_values, 0, "+")
hdw.get_deri(deri[1], phi, bdry_values, 0, "-")
u2_form = 3.0/4.0*temp_phi + 1.0/4.0*phi - 1.0/4.0*dt*Hhat
project(u2_form, phi.function_space(), function=phi)
#compute final u, stored in var_list
bdry_values = bdry.get_bdry_values(exact_phi)
hdw.get_deri(deri[0], phi, bdry_values, 0, "+")
hdw.get_deri(deri[1], phi, bdry_values, 0, "-")
final_form = 1.0/3.0*temp_phi + 2.0/3.0*phi - 2.0/3.0*dt*Hhat
project(final_form, phi.function_space(), function=phi)
def rk3(var_list, exact_characteristic_field_values, temp_var_list, deri_list,
form_packs, func_packs, dt):
auxi_list = func_packs[1]
rhs_forms = form_packs[-1]
rhs_list = func_packs[-1]
#compute u1, stored in var_list
for idx in range(len(form_packs) - 1):
hdw.project_functions(form_packs[idx], func_packs[idx])
bdry_values = bdry.get_bdry_values(var_list, auxi_list,
exact_characteristic_field_values)
for idx in range(len(var_list)):
hdw.get_deri(deri_list[idx][0], var_list[idx], bdry_values[idx], 0,
"+")
hdw.get_deri(deri_list[idx][1], var_list[idx], bdry_values[idx], 0,
"-")
hdw.project_functions(rhs_forms, rhs_list)
u1_forms = [
temp_var_list[idx] + dt * rhs_list[idx] for idx in range(len(var_list))
]
hdw.project_functions(u1_forms, var_list)
#compute u2, stored in var_list
for idx in range(len(form_packs) - 1):
hdw.project_functions(form_packs[idx], func_packs[idx])
bdry_values = bdry.get_bdry_values(var_list, auxi_list,
exact_characteristic_field_values)
for idx in range(len(var_list)):
hdw.get_deri(deri_list[idx][0], var_list[idx], bdry_values[idx], 0,
"+")
hdw.get_deri(deri_list[idx][1], var_list[idx], bdry_values[idx], 0,
"-")
hdw.project_functions(rhs_forms, rhs_list)
u2_forms = [
3.0 / 4.0 * temp_var_list[idx] + 1.0 / 4.0 * var_list[idx] +
1.0 / 4.0 * dt * rhs_list[idx] for idx in range(len(var_list))
]
hdw.project_functions(u2_forms, var_list)
#compute final u, stored in var_list
for idx in range(len(form_packs) - 1):
hdw.project_functions(form_packs[idx], func_packs[idx])
bdry_values = bdry.get_bdry_values(var_list, auxi_list,
exact_characteristic_field_values)
for idx in range(len(var_list)):
hdw.get_deri(deri_list[idx][0], var_list[idx], bdry_values[idx], 0,
"+")
hdw.get_deri(deri_list[idx][1], var_list[idx], bdry_values[idx], 0,
"-")
hdw.project_functions(rhs_forms, rhs_list)
final_forms = [
1.0 / 3.0 * temp_var_list[idx] + 2.0 / 3.0 * var_list[idx] +
2.0 / 3.0 * dt * rhs_list[idx] for idx in range(len(var_list))
]
hdw.project_functions(final_forms, var_list)
def rk2(var_list, exact_characteristic_field_values, temp_var_list, deri_list,
form_packs, func_packs, dt):
auxi_list = func_packs[1]
rhs_forms = form_packs[-1]
rhs_list = func_packs[-1]
for dummy in range(2):
for idx in range(len(form_packs) - 1):
hdw.project_functions(form_packs[idx], func_packs[idx])
bdry_values = bdry.get_bdry_values(var_list, auxi_list,
exact_characteristic_field_values)
for idx in range(len(var_list)):
hdw.get_deri(deri_list[idx][0], var_list[idx], bdry_values[idx], 0,
"+")
hdw.get_deri(deri_list[idx][1], var_list[idx], bdry_values[idx], 0,
"-")
hdw.project_functions(rhs_forms, rhs_list)
dt_forms = [
var_list[idx] + dt * rhs_list[idx] for idx in range(len(var_list))
]
hdw.project_functions(dt_forms, var_list)
final_forms = [
0.5 * (temp_var_list[idx] + var_list[idx])
for idx in range(len(var_list))
]
hdw.project_functions(final_forms, var_list)
def rk2(phi, exact_phi, temp_phi, deri, Hhat, dt):
temp_phi.assign(phi)
for dummy in range(2):
bdry_values = bdry.get_bdry_values(exact_phi)
hdw.get_deri(deri[0], phi, bdry_values, 0, "+")
hdw.get_deri(deri[1], phi, bdry_values, 0, "-")
dt_form = phi - dt*Hhat
project(dt_form, phi.function_space(), function=phi)
final_form = 0.5*(temp_phi + phi)
project(final_form, phi.function_space(), function=phi)