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Laura Christine Kühle
Troubled Cell Detection
Commits
6c9f4f80
Commit
6c9f4f80
authored
5 years ago
by
Laura Christine Kühle
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# -*- coding: utf-8 -*-
"""
@author: Laura C. Kühle
d = detail coefficient (rename?)
other A (from M) = ? (Is it the same???)
A = basis_projection_left
M1 = wavelet_projection_left
phi = DG basis vector
psi = wavelet vector
TODO: Find better names for A, B, M1, and M2
TODO: Contemplate how to handle closing brackets
\
(end of line?, indented in new line?) -> Done (in line seems to be fine)
TODO: Contemplate giving option to change number of iterations for history
\
-> Done (history_threshold)
TODO: Rename counter -> Done (iteration)
TODO: Investigate whether list comprehension improves runtime
\
(compared to for-loops) -> Done (not really but more compact)
"""
import
numpy
as
np
from
sympy
import
Symbol
,
integrate
from
Vectors_of_Polynomials
import
OrthonormalLegendre
,
AlpertsWavelet
x
=
Symbol
(
'
x
'
)
xi
=
Symbol
(
'
z
'
)
class
UpdateScheme
(
object
):
def
__init__
(
self
,
detector
,
limiter
,
init_cond
,
mesh
,
wave_speed
,
polynom_degree
,
num_grid_cells
,
final_time
,
history_threshold
,
left_bound
,
right_bound
):
# Unpack positional arguments
self
.
detector
=
detector
self
.
limiter
=
limiter
self
.
init_cond
=
init_cond
self
.
mesh
=
mesh
self
.
wave_speed
=
wave_speed
self
.
polynom_degree
=
polynom_degree
self
.
num_grid_cells
=
num_grid_cells
self
.
final_time
=
final_time
self
.
history_threshold
=
history_threshold
self
.
left_bound
=
left_bound
self
.
right_bound
=
right_bound
self
.
_reset
()
pass
def
get_name
(
self
):
return
self
.
name
def
get_troubled_cell_history
(
self
):
return
self
.
troubled_cell_history
def
get_time_history
(
self
):
return
self
.
time_history
def
get_wavelet_coeffs
(
self
,
projection
=
None
):
if
projection
is
None
:
return
self
.
multiwavelet_coeffs
else
:
return
self
.
_calculate_wavelet_coeffs
(
projection
)
def
step
(
self
,
projection
,
cfl_number
,
time
):
self
.
original_projection
=
projection
self
.
current_projection
=
projection
self
.
cfl_number
=
cfl_number
self
.
time
=
time
self
.
_apply_stability_method
()
self
.
iteration
+=
1
if
(
self
.
iteration
%
self
.
history_threshold
)
==
0
:
self
.
troubled_cell_history
.
append
(
self
.
troubled_cells
)
self
.
time_history
.
append
(
self
.
time
)
return
self
.
current_projection
,
self
.
troubled_cells
def
_reset
(
self
):
# Set fixed basis and wavelet vectors
self
.
basis
=
OrthonormalLegendre
(
self
.
polynom_degree
).
get_vector
(
x
)
self
.
wavelet
=
AlpertsWavelet
(
self
.
polynom_degree
).
get_vector
(
x
)
# Set additional necessary fixed instance variables
self
.
interval_len
=
self
.
right_bound
-
self
.
left_bound
self
.
cell_len
=
self
.
interval_len
/
self
.
num_grid_cells
self
.
M1
=
self
.
_set_multiwavelet_matrix
(
xi
,
-
0.5
*
(
xi
-
1
),
True
)
self
.
M2
=
self
.
_set_multiwavelet_matrix
(
xi
,
0.5
*
(
xi
+
1
),
False
)
# Set matrix A
matrix
=
[]
for
i
in
range
(
self
.
polynom_degree
+
1
):
new_row
=
[]
for
j
in
range
(
self
.
polynom_degree
+
1
):
new_entry
=
-
1.0
if
((
j
<
i
)
&
((
i
+
j
)
%
2
==
1
)):
new_entry
=
1.0
new_row
.
append
(
new_entry
*
np
.
sqrt
((
i
+
0.5
)
*
(
j
+
0.5
)))
matrix
.
append
(
new_row
)
self
.
A
=
np
.
array
(
matrix
)
# former: inv_mass @ np.array(matrix)
# Set matrix B
matrix
=
[]
for
i
in
range
(
self
.
polynom_degree
+
1
):
new_row
=
[]
for
j
in
range
(
self
.
polynom_degree
+
1
):
new_entry
=
np
.
sqrt
((
i
+
0.5
)
*
(
j
+
0.5
))
*
(
-
1.0
)
**
i
new_row
.
append
(
new_entry
)
matrix
.
append
(
new_row
)
self
.
B
=
np
.
array
(
matrix
)
# former: inv_mass @ np.array(matrix)
# Initialize temporary instance variables
self
.
original_projection
=
[]
self
.
current_projection
=
[]
self
.
right_hand_side
=
[]
self
.
multiwavelet_coeffs
=
[]
self
.
troubled_cells
=
[]
self
.
troubled_cell_history
=
[]
self
.
time_history
=
[]
self
.
cfl_number
=
0
self
.
time
=
0
self
.
iteration
=
0
def
_set_multiwavelet_matrix
(
self
,
first_param
,
second_param
,
is_M1
):
matrix
=
[]
for
i
in
range
(
self
.
polynom_degree
+
1
):
row
=
[]
for
j
in
range
(
self
.
polynom_degree
+
1
):
entry
=
integrate
(
self
.
basis
[
i
].
subs
(
x
,
first_param
)
*
self
.
wavelet
[
j
].
subs
(
x
,
second_param
),
(
xi
,
-
1
,
1
))
if
(
is_M1
):
entry
=
entry
*
(
-
1
)
**
(
j
+
self
.
polynom_degree
+
1
)
row
.
append
(
np
.
float64
(
entry
))
matrix
.
append
(
row
)
return
matrix
def
_update_wavelet_coeffs
(
self
):
projection
=
self
.
current_projection
[:,
1
:
-
1
]
self
.
multiwavelet_coeffs
=
self
.
_calculate_wavelet_coeffs
(
projection
)
def
_calculate_wavelet_coeffs
(
self
,
projection
):
transposed_vector
=
np
.
transpose
(
projection
)
output_matrix
=
[]
for
i
in
range
(
int
(
len
(
projection
[
0
])
/
2
)):
new_entry
=
0.5
*
(
transposed_vector
[
2
*
i
]
@
self
.
M1
+
transposed_vector
[
2
*
i
+
1
]
@
self
.
M2
)
output_matrix
.
append
(
new_entry
)
return
np
.
transpose
(
np
.
array
(
output_matrix
))
def
_apply_limiter
(
self
):
self
.
_update_wavelet_coeffs
()
self
.
troubled_cells
=
self
.
detector
.
get_cells
(
self
.
multiwavelet_coeffs
,
self
.
current_projection
)
new_projection
=
self
.
current_projection
.
copy
()
for
cell
in
self
.
troubled_cells
:
np
.
transpose
(
new_projection
)[
cell
]
=
self
.
limiter
.
apply
(
self
.
current_projection
,
cell
)
self
.
current_projection
=
new_projection
def
_enforce_boundary_condition
(
self
):
transposed_projection
=
np
.
transpose
(
self
.
current_projection
)
transposed_projection
[
0
]
=
transposed_projection
[
self
.
num_grid_cells
]
transposed_projection
[
self
.
num_grid_cells
+
1
]
=
transposed_projection
[
1
]
self
.
current_projection
=
np
.
transpose
(
transposed_projection
)
class
SSPRK3
(
UpdateScheme
):
def
__init__
(
self
,
detector
,
limiter
,
init_cond
,
mesh
,
wave_speed
,
polynom_degree
,
num_grid_cells
,
final_time
,
history_threshold
,
left_bound
,
right_bound
):
# Set name of update scheme
self
.
name
=
'
SSPRK3
'
super
().
__init__
(
detector
,
limiter
,
init_cond
,
mesh
,
wave_speed
,
polynom_degree
,
num_grid_cells
,
final_time
,
history_threshold
,
left_bound
,
right_bound
)
# Override method of superclass
def
_apply_stability_method
(
self
):
self
.
_apply_first_step
()
self
.
_apply_limiter
()
self
.
_enforce_boundary_condition
()
self
.
_apply_second_step
()
self
.
_apply_limiter
()
self
.
_enforce_boundary_condition
()
self
.
_apply_third_step
()
self
.
_apply_limiter
()
self
.
_enforce_boundary_condition
()
def
_update_right_hand_side
(
self
):
# Transpose projection for easier calculation
transposed_projection
=
np
.
transpose
(
self
.
current_projection
)
# Initialze vector and set first entry to accommodate for ghost cell
right_hand_side
=
[
0
]
for
j
in
range
(
self
.
num_grid_cells
):
right_hand_side
.
append
(
2
*
(
self
.
A
@
transposed_projection
[
j
+
1
]
+
self
.
B
@
transposed_projection
[
j
]))
# Set ghost cells to respective value
right_hand_side
[
0
]
=
right_hand_side
[
self
.
num_grid_cells
]
right_hand_side
.
append
(
right_hand_side
[
1
])
self
.
right_hand_side
=
np
.
transpose
(
right_hand_side
)
def
_apply_first_step
(
self
):
self
.
_update_right_hand_side
()
self
.
current_projection
=
self
.
original_projection
\
+
(
self
.
cfl_number
*
self
.
right_hand_side
)
def
_apply_second_step
(
self
):
self
.
_update_right_hand_side
()
self
.
current_projection
=
1
/
4
*
(
3
*
self
.
original_projection
+
(
self
.
current_projection
+
self
.
cfl_number
*
self
.
right_hand_side
))
def
_apply_third_step
(
self
):
self
.
_update_right_hand_side
()
self
.
current_projection
=
1
/
3
*
(
self
.
original_projection
+
2
*
(
self
.
current_projection
+
self
.
cfl_number
*
self
.
right_hand_side
))
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