def test_mesh_to_mesh_1d_dirichlet():
"""
A simple test program to test dirichlet interpolation order in space
"""
# initialize problem parameters
problem_params = {}
problem_params['nu'] = 0.1 # diffusion coefficient
problem_params['freq'] = 3 # frequency for the test value
# initialize transfer parameters
space_transfer_params = {}
space_transfer_params['rorder'] = 2
iorder_list = [2,4,6,8]
nvars_fine_list = [2**p-1 for p in range(5,9)]
# set up dictionary to store results (plus lists)
results = {}
results['nvars_fine_list'] = nvars_fine_list
results['iorder_list'] = iorder_list
# loop over interpolation orders and number of DOFs
for iorder in iorder_list:
space_transfer_params['iorder'] = iorder
for nvars_fine in nvars_fine_list:
# instantiate fine problem
problem_params['nvars'] = nvars_fine # number of degrees of freedom
Pfine = heat1d(problem_params=problem_params, dtype_u=mesh, dtype_f=mesh)
# instantiate coarse problem
problem_params['nvars'] = int((nvars_fine + 1) / 2.0 - 1)
Pcoarse = heat1d(problem_params=problem_params, dtype_u=mesh, dtype_f=mesh)
# instantiate spatial interpolation
T = mesh_to_mesh(fine_prob=Pfine, coarse_prob=Pcoarse, params=space_transfer_params)
# set exact fine solution to compare with
uexact_fine = Pfine.u_exact(t=0)
# set exact coarse solution as source
uexact_coarse = Pcoarse.u_exact(t=0)
# do the interpolation/prolongation
uinter = T.prolong(uexact_coarse)
# compute error and store
err = abs(uinter-uexact_fine)
id = ID(nvars_fine=nvars_fine, iorder=iorder)
results[id] = err
orders = get_accuracy_orders(results)
for p in range(len(orders)):
# print(abs(orders[p][1]-orders[p][2])/orders[p][1])
assert abs(orders[p][1]-orders[p][2])/orders[p][1] < 0.151, 'ERROR: did not get expected orders for interpolation, got %s' %str(orders[p])
def main():
"""
A simple test program to test interpolation order in space
"""
# initialize problem parameters
problem_params = dict()
problem_params['nu'] = 0.1 # diffusion coefficient
problem_params['freq'] = 3 # frequency for the test value
# initialize transfer parameters
space_transfer_params = dict()
space_transfer_params['rorder'] = 2
space_transfer_params['iorder'] = 4
nvars_fine_list = [2**p - 1 for p in range(5, 10)]
# set up dictionary to store results (plus lists)
results = dict()
results['nvars_list'] = nvars_fine_list
for nvars_fine in nvars_fine_list:
print('Working on nvars_fine = %4i...' % nvars_fine)
# instantiate fine problem
problem_params['nvars'] = nvars_fine # number of degrees of freedom
Pfine = heat1d(problem_params=problem_params,
dtype_u=mesh,
dtype_f=mesh)
# instantiate coarse problem using half of the DOFs
problem_params['nvars'] = int((nvars_fine + 1) / 2.0 - 1)
Pcoarse = heat1d(problem_params=problem_params,
dtype_u=mesh,
dtype_f=mesh)
# instantiate spatial interpolation
T = mesh_to_mesh(fine_prob=Pfine,
coarse_prob=Pcoarse,
params=space_transfer_params)
# set exact fine solution to compare with
xvalues_fine = np.array([(i + 1) * Pfine.dx
for i in range(Pfine.params.nvars)])
uexact_fine = Pfine.dtype_u(0)
uexact_fine.values = np.sin(np.pi * Pfine.params.freq * xvalues_fine)
# set exact coarse solution as source
xvalues_coarse = np.array([(i + 1) * Pcoarse.dx
for i in range(Pcoarse.params.nvars)])
uexact_coarse = Pfine.dtype_u(0)
uexact_coarse.values = np.sin(np.pi * Pcoarse.params.freq *
xvalues_coarse)
# do the interpolation/prolongation
uinter = T.prolong(uexact_coarse)
# compute error and store
id = ID(nvars_fine=nvars_fine)
results[id] = abs(uinter - uexact_fine)
# print out and check
print('Running order checks...')
orders = get_accuracy_order(results)
f = open('step_4_A_out.txt', 'w')
for p in range(len(orders)):
out = 'Expected order %2i, got order %5.2f, deviation of %5.2f%%' \
% (space_transfer_params['iorder'], orders[p],
100 * abs(space_transfer_params['iorder'] - orders[p]) / space_transfer_params['iorder'])
f.write(out + '\n')
print(out)
assert abs(space_transfer_params['iorder'] - orders[p]) / space_transfer_params['iorder'] < 0.05, \
'ERROR: did not get expected orders for interpolation, got %s' % str(orders[p])
f.close()
print('...got what we expected!')