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Laura Christine Kühle
Troubled Cell Detection
Commits
64e74022
Commit
64e74022
authored
May 10, 2022
by
Laura Christine Kühle
Browse files
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Plain Diff
Contained polynomial degree in basis.
parent
ed0a0574
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Changes
4
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4 changed files
Basis_Function.py
+7
-0
7 additions, 0 deletions
Basis_Function.py
DG_Approximation.py
+12
-13
12 additions, 13 deletions
DG_Approximation.py
Plotting.py
+20
-27
20 additions, 27 deletions
Plotting.py
Troubled_Cell_Detector.py
+4
-6
4 additions, 6 deletions
Troubled_Cell_Detector.py
with
43 additions
and
46 deletions
Basis_Function.py
+
7
−
0
View file @
64e74022
...
...
@@ -21,6 +21,8 @@ class Basis:
Attributes
----------
polynomial degree : int
Polynomial degree.
basis : ndarray
Array of basis.
wavelet : ndarray
...
...
@@ -47,6 +49,11 @@ class Basis:
"""
self
.
_polynomial_degree
=
polynomial_degree
@property
def
polynomial_degree
(
self
):
"""
Return polynomial degree.
"""
return
self
.
_polynomial_degree
@property
@cache
def
basis
(
self
):
...
...
This diff is collapsed.
Click to expand it.
DG_Approximation.py
+
12
−
13
View file @
64e74022
...
...
@@ -7,13 +7,15 @@ TODO: Contemplate saving 5-CV split and evaluating models separately
TODO: Contemplate separating cell average and reconstruction calculations
completely
TODO: Contemplate removing Methods section from class docstring
TODO: Contemplate moving stiffness and boundary matrix from update scheme
to basis
Urgent:
TODO: Investigate protected vs. public variables -> Done
TODO: Investigate decorators and properties -> Done
TODO: Investigate how to make variables read-only -> Done
TODO: Replace getter with property attributes for basis -> Done
TODO: Contain polynomial degree in basis
TODO: Contain polynomial degree in basis
-> Done
TODO: Improve docstring for Basis class
TODO: Enforce abstract classes/methods (abc.ABC, abc.abstractmethod)
TODO: Introduce Mesh class
...
...
@@ -154,7 +156,6 @@ class DGScheme:
"""
# Unpack keyword arguments
self
.
_wave_speed
=
kwargs
.
pop
(
'
wave_speed
'
,
1
)
self
.
_polynomial_degree
=
kwargs
.
pop
(
'
polynomial_degree
'
,
2
)
self
.
_cfl_number
=
kwargs
.
pop
(
'
cfl_number
'
,
0.2
)
self
.
_num_grid_cells
=
kwargs
.
pop
(
'
num_grid_cells
'
,
64
)
self
.
_final_time
=
kwargs
.
pop
(
'
final_time
'
,
1
)
...
...
@@ -173,6 +174,9 @@ class DGScheme:
self
.
_quadrature_config
=
kwargs
.
pop
(
'
quadrature_config
'
,
{})
self
.
_update_scheme
=
kwargs
.
pop
(
'
update_scheme
'
,
'
SSPRK3
'
)
polynomial_degree
=
kwargs
.
pop
(
'
polynomial_degree
'
,
2
)
self
.
_basis
=
OrthonormalLegendre
(
polynomial_degree
)
# Throw an error if there are extra keyword arguments
if
len
(
kwargs
)
>
0
:
extra
=
'
,
'
.
join
(
'"
%s
"'
%
k
for
k
in
list
(
kwargs
.
keys
()))
...
...
@@ -206,12 +210,11 @@ class DGScheme:
self
.
_detector
=
getattr
(
Troubled_Cell_Detector
,
self
.
_detector
)(
config
=
self
.
_detector_config
,
mesh
=
self
.
_mesh
,
wave_speed
=
self
.
_wave_speed
,
num_grid_cells
=
self
.
_num_grid_cells
,
polynomial_degree
=
self
.
_polynomial_degree
,
final_time
=
self
.
_final_time
,
left_bound
=
self
.
_left_bound
,
right_bound
=
self
.
_right_bound
,
basis
=
self
.
_basis
,
init_cond
=
self
.
_init_cond
,
quadrature
=
self
.
_quadrature
)
self
.
_update_scheme
=
getattr
(
Update_Scheme
,
self
.
_update_scheme
)(
polynomial_degree
=
self
.
_
polynomial_degree
,
polynomial_degree
=
polynomial_degree
,
num_grid_cells
=
self
.
_num_grid_cells
,
detector
=
self
.
_detector
,
limiter
=
self
.
_limiter
)
...
...
@@ -233,8 +236,7 @@ class DGScheme:
projection
=
do_initial_projection
(
initial_condition
=
self
.
_init_cond
,
basis
=
self
.
_basis
,
quadrature
=
self
.
_quadrature
,
num_grid_cells
=
self
.
_num_grid_cells
,
left_bound
=
self
.
_left_bound
,
right_bound
=
self
.
_right_bound
,
polynomial_degree
=
self
.
_polynomial_degree
)
left_bound
=
self
.
_left_bound
,
right_bound
=
self
.
_right_bound
)
time_step
=
abs
(
self
.
_cfl_number
*
self
.
_cell_len
/
self
.
_wave_speed
)
...
...
@@ -281,7 +283,6 @@ class DGScheme:
# Set additional necessary instance variables
self
.
_interval_len
=
self
.
_right_bound
-
self
.
_left_bound
self
.
_cell_len
=
self
.
_interval_len
/
self
.
_num_grid_cells
self
.
_basis
=
OrthonormalLegendre
(
self
.
_polynomial_degree
)
# Set additional necessary config parameters
self
.
_limiter_config
[
'
cell_len
'
]
=
self
.
_cell_len
...
...
@@ -323,7 +324,7 @@ class DGScheme:
initial_condition
=
initial_condition
,
basis
=
self
.
_basis
,
quadrature
=
self
.
_quadrature
,
num_grid_cells
=
self
.
_num_grid_cells
,
left_bound
=
self
.
_left_bound
,
right_bound
=
self
.
_right_bound
,
polynomial_degree
=
self
.
_polynomial_degree
,
adjustment
=
adjustment
)
adjustment
=
adjustment
)
return
self
.
_basis
.
calculate_cell_average
(
projection
=
projection
[:,
1
:
-
1
],
stencil_length
=
stencil_length
,
...
...
@@ -332,7 +333,7 @@ class DGScheme:
def
do_initial_projection
(
initial_condition
,
basis
,
quadrature
,
num_grid_cells
,
left_bound
,
right_bound
,
polynomial_degree
,
adjustment
=
0
):
adjustment
=
0
):
"""
Calculates initial projection.
Calculates a projection at time step 0 and adds ghost cells on both
...
...
@@ -352,8 +353,6 @@ def do_initial_projection(initial_condition, basis, quadrature,
Left boundary of interval.
right_bound : float
Right boundary of interval.
polynomial_degree : int
Polynomial degree.
adjustment: float, optional
Extent of adjustment of each evaluation point in x-direction.
Default: 0.
...
...
@@ -362,7 +361,7 @@ def do_initial_projection(initial_condition, basis, quadrature,
-------
ndarray
Matrix containing projection of size (N+2, p+1) with N being the
number of grid cells and p being the polynomial degree.
number of grid cells and p being the polynomial degree
of the basis
.
"""
# Initialize matrix and set first entry to accommodate for ghost cell
...
...
@@ -374,7 +373,7 @@ def do_initial_projection(initial_condition, basis, quadrature,
new_row
=
[]
eval_point
=
left_bound
+
(
cell
+
0.5
)
*
cell_len
for
degree
in
range
(
polynomial_degree
+
1
):
for
degree
in
range
(
basis
.
polynomial_degree
+
1
):
new_row
.
append
(
np
.
float64
(
sum
(
initial_condition
.
calculate
(
eval_point
+
cell_len
/
2
*
quadrature
.
get_eval_points
()[
point
]
-
adjustment
)
...
...
This diff is collapsed.
Click to expand it.
Plotting.py
+
20
−
27
View file @
64e74022
...
...
@@ -124,10 +124,9 @@ def plot_shock_tube(num_grid_cells: int, troubled_cell_history: list,
plt
.
title
(
'
Shock Tubes
'
)
def
plot_details
(
fine_projection
:
ndarray
,
fine_mesh
:
ndarray
,
coarse_projection
:
ndarray
,
basis
:
ndarray
,
wavelet
:
ndarray
,
multiwavelet_coeffs
:
ndarray
,
num_coarse_grid_cells
:
int
,
polynomial_degree
:
int
)
->
None
:
def
plot_details
(
fine_projection
:
ndarray
,
fine_mesh
:
ndarray
,
basis
:
Basis
,
coarse_projection
:
ndarray
,
multiwavelet_coeffs
:
ndarray
,
num_coarse_grid_cells
:
int
)
->
None
:
"""
Plots details of projection to coarser mesh.
Parameters
...
...
@@ -136,35 +135,32 @@ def plot_details(fine_projection: ndarray, fine_mesh: ndarray,
Matrix of projection for each polynomial degree.
fine_mesh : ndarray
List of evaluation points for fine mesh.
basis : ndarray
Basis vector for calculation.
wavelet : ndarray
Wavelet vector for calculation.
basis: Basis object
Basis used for calculation.
multiwavelet_coeffs : ndarray
Matrix of multiwavelet coefficients.
num_coarse_grid_cells : int
Number of cells in the coarse mesh (half the cells of the fine mesh).
Usually exponential of 2.
polynomial_degree : int
Polynomial degree.
"""
averaged_projection
=
[[
coarse_projection
[
degree
][
cell
]
*
basis
[
degree
].
subs
(
x
,
value
)
*
basis
.
basis
[
degree
].
subs
(
x
,
value
)
for
cell
in
range
(
num_coarse_grid_cells
)
for
value
in
[
-
0.5
,
0.5
]]
for
degree
in
range
(
polynomial_degree
+
1
)]
for
degree
in
range
(
basis
.
polynomial_degree
+
1
)]
wavelet_projection
=
[[
multiwavelet_coeffs
[
degree
][
cell
]
*
wavelet
[
degree
].
subs
(
z
,
0.5
)
*
value
*
basis
.
wavelet
[
degree
].
subs
(
z
,
0.5
)
*
value
for
cell
in
range
(
num_coarse_grid_cells
)
for
value
in
[(
-
1
)
**
(
polynomial_degree
for
value
in
[(
-
1
)
**
(
basis
.
polynomial_degree
+
degree
+
1
),
1
]]
for
degree
in
range
(
polynomial_degree
+
1
)]
for
degree
in
range
(
basis
.
polynomial_degree
+
1
)]
projected_coarse
=
np
.
sum
(
averaged_projection
,
axis
=
0
)
projected_fine
=
np
.
sum
([
fine_projection
[
degree
]
*
basis
[
degree
].
subs
(
x
,
0
)
for
degree
in
range
(
polynomial_degree
+
1
)],
projected_fine
=
np
.
sum
([
fine_projection
[
degree
]
*
basis
.
basis
[
degree
].
subs
(
x
,
0
)
for
degree
in
range
(
basis
.
polynomial_degree
+
1
)],
axis
=
0
)
projected_wavelet_coeffs
=
np
.
sum
(
wavelet_projection
,
axis
=
0
)
...
...
@@ -352,6 +348,7 @@ def plot_approximation_results(data_file: str, directory: str, plot_name: str,
# Decode all ndarrays by converting lists
approx_stats
=
{
key
:
decode_ndarray
(
approx_stats
[
key
])
for
key
in
approx_stats
.
keys
()}
approx_stats
.
pop
(
'
polynomial_degree
'
)
# Plot exact/approximate results, errors, shock tubes,
# and any detector-dependant plots
...
...
@@ -375,7 +372,7 @@ def plot_approximation_results(data_file: str, directory: str, plot_name: str,
def
plot_results
(
projection
:
ndarray
,
troubled_cell_history
:
list
,
time_history
:
list
,
mesh
:
ndarray
,
num_grid_cells
:
int
,
polynomial_degree
:
int
,
wave_speed
:
float
,
final_time
:
float
,
wave_speed
:
float
,
final_time
:
float
,
left_bound
:
float
,
right_bound
:
float
,
basis
:
Basis
,
quadrature
:
Quadrature
,
init_cond
:
InitialCondition
,
colors
:
dict
=
None
,
coarse_projection
:
ndarray
=
None
,
...
...
@@ -400,8 +397,6 @@ def plot_results(projection: ndarray, troubled_cell_history: list,
List of mesh valuation points.
num_grid_cells : int
Number of cells in the mesh. Usually exponential of 2.
polynomial_degree : int
Polynomial degree.
wave_speed : float
Speed of wave in rightward direction.
final_time : float
...
...
@@ -444,7 +439,7 @@ def plot_results(projection: ndarray, troubled_cell_history: list,
init_cond
)
approx
=
calculate_approximate_solution
(
projection
[:,
1
:
-
1
],
quadrature
.
get_eval_points
(),
polynomial_degree
,
basis
.
basis
)
basis
.
polynomial_degree
,
basis
.
basis
)
# Plot multiwavelet solution (fine and coarse grid)
if
coarse_projection
is
not
None
:
...
...
@@ -460,17 +455,15 @@ def plot_results(projection: ndarray, troubled_cell_history: list,
init_cond
)
coarse_approx
=
calculate_approximate_solution
(
coarse_projection
,
quadrature
.
get_eval_points
(),
polynomial_degree
,
basis
.
basis
)
basis
.
polynomial_degree
,
basis
.
basis
)
plot_solution_and_approx
(
coarse_grid
,
coarse_exact
,
coarse_approx
,
colors
[
'
coarse_exact
'
],
colors
[
'
coarse_approx
'
])
# Plot multiwavelet details
num_coarse_grid_cells
=
num_grid_cells
//
2
plot_details
(
projection
[:,
1
:
-
1
],
mesh
[
2
:
-
2
],
coarse_projection
,
basis
.
basis
,
basis
.
wavelet
,
multiwavelet_coeffs
,
num_coarse_grid_cells
,
polynomial_degree
)
plot_details
(
projection
[:,
1
:
-
1
],
mesh
[
2
:
-
2
],
basis
,
coarse_projection
,
multiwavelet_coeffs
,
num_coarse_grid_cells
)
plot_solution_and_approx
(
grid
,
exact
,
approx
,
colors
[
'
fine_exact
'
],
...
...
@@ -491,7 +484,7 @@ def plot_results(projection: ndarray, troubled_cell_history: list,
plot_semilog_error
(
grid
,
pointwise_error
)
plot_error
(
grid
,
exact
,
approx
)
print
(
'
p =
'
,
polynomial_degree
)
print
(
'
p =
'
,
basis
.
polynomial_degree
)
print
(
'
N =
'
,
num_grid_cells
)
print
(
'
maximum error =
'
,
max_error
)
...
...
This diff is collapsed.
Click to expand it.
Troubled_Cell_Detector.py
+
4
−
6
View file @
64e74022
...
...
@@ -37,7 +37,7 @@ class TroubledCellDetector:
"""
def
__init__
(
self
,
config
,
init_cond
,
quadrature
,
basis
,
mesh
,
wave_speed
=
1
,
polynomial_degree
=
2
,
num_grid_cells
=
64
,
wave_speed
=
1
,
num_grid_cells
=
64
,
final_time
=
1
,
left_bound
=-
1
,
right_bound
=
1
):
"""
Initializes TroubledCellDetector.
...
...
@@ -55,8 +55,6 @@ class TroubledCellDetector:
List of mesh valuation points.
wave_speed : float, optional
Speed of wave in rightward direction. Default: 1.
polynomial_degree : int, optional
Polynomial degree. Default: 2.
num_grid_cells : int, optional
Number of cells in the mesh. Usually exponential of 2. Default: 64.
final_time : float, optional
...
...
@@ -69,7 +67,6 @@ class TroubledCellDetector:
"""
self
.
_mesh
=
mesh
self
.
_wave_speed
=
wave_speed
self
.
_polynomial_degree
=
polynomial_degree
self
.
_num_grid_cells
=
num_grid_cells
self
.
_final_time
=
final_time
self
.
_left_bound
=
left_bound
...
...
@@ -113,7 +110,7 @@ class TroubledCellDetector:
'
num_grid_cells
'
:
self
.
_num_grid_cells
,
'
mesh
'
:
self
.
_mesh
,
'
final_time
'
:
self
.
_final_time
,
'
left_bound
'
:
self
.
_left_bound
,
'
right_bound
'
:
self
.
_right_bound
,
'
polynomial_degree
'
:
self
.
_polynomial_degree
'
polynomial_degree
'
:
self
.
_
basis
.
polynomial_degree
}
...
...
@@ -513,7 +510,8 @@ class Theoretical(WaveletDetector):
"""
max_value
=
max
(
abs
(
multiwavelet_coeffs
[
degree
][
cell
])
for
degree
in
range
(
self
.
_polynomial_degree
+
1
))
/
max_avg
for
degree
in
range
(
self
.
_basis
.
polynomial_degree
+
1
))
/
max_avg
eps
=
self
.
_cutoff_factor
\
/
(
self
.
_cell_len
*
self
.
_num_coarse_grid_cells
*
2
)
...
...
This diff is collapsed.
Click to expand it.
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