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Improve segment_ratios by proposing an optimized end_length_ratio #245

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Improve segment_ratios by proposing an optimized end_length_ratio #245

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25 changes: 23 additions & 2 deletions pygfunction/utilities.py
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Original file line number Diff line number Diff line change
Expand Up @@ -71,7 +71,8 @@ def exp1(x):
return E1


def segment_ratios(nSegments, end_length_ratio=0.02):

def segment_ratios(nSegments, end_length_ratio=None):
"""
Discretize a borehole into segments of different lengths using a
geometrically expanding mesh from the provided end-length-ratio towards the
Expand All @@ -87,7 +88,11 @@ def segment_ratios(nSegments, end_length_ratio=0.02):
end_length_ratio: float, optional
The ratio of the height of the borehole that accounts for the end
segment lengths.
Default is 0.02.
Default is dependent on the number of segments,
for number of segments between 3 and 34 the end_length_ratio
is taken from a list with proposed values that in most cases
minimize the relative error of the g-function.
For number of segments between 35 and 500 the default is 0.002.

Returns
-------
Expand All @@ -105,6 +110,22 @@ def segment_ratios(nSegments, end_length_ratio=0.02):
extraction boreholes. PhD Thesis. University of Lund, Department of
Mathematical Physics. Lund, Sweden.
"""
_optimal_elr = [0.0498, 0.0366, 0.0212, 0.0176, 0.0108, 0.0093,
0.0057, 0.0054, 0.0042, 0.0039, 0.0032, 0.0027,
0.0026, 0.0021, 0.0013, 0.001, 0.0009, 0.0011,
0.0013, 0.0014, 0.0015, 0.0016, 0.0017, 0.0017,
0.0018, 0.0018, 0.0018, 0.0019, 0.0019, 0.0019,
0.0019, 0.0019, 0.002]

# For nSegments between 3 and 34, the proposed end_length_ratio is taken
# from _optimal_elr.
if end_length_ratio == None:
if nSegments >= 3 and nSegments <= 34:
end_length_ratio = _optimal_elr[nSegments - 3]
else:
# For nSegments between 35 and 500, the end_length_ratio is 0.002
end_length_ratio = _optimal_elr[-1]

def is_even(n):
"Returns True if n is even."
return not(n & 0x1)
Expand Down