Fix bug on non-diagonal tensor components of prisms #27
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The non-diagonal tensor components of the prism have a bug due to a wrong evaluation of the logarithmic function. Add two tests that catch the bug on the g_en component.
Implement a modified version of the log function proposed by Fukushima (2020). It now takes both the shifted coordinate and the distance r (instead of the whole argument of the log function) since it returns slightly different things based on the value of those parameters.
santisoler
changed the title
After evaluating the limit of g_en on points above the vertices I found that it can be written as ln(|z1| / |z2|) which translates into [- ln(|z2|) ] - [- ln(|z1|)]. So for x < 0 and r = -x i the safe_log returns -ln(|x|).
Apply the new derived formula not from the limit, but directly from inverting the z axis.
Instead of checking through directions, check with observation points around the observation point that could have wrong results.
santisoler
commented
Dec 12, 2022
santisoler
commented
Dec 12, 2022
|
The additional tests corroborate that this PR fixes the bug. I'm merging this 🚀 |
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Fix a bug on the non-diagonal tensor components of the prism due to a wrong
evaluation of the logarithmic function. Add two tests that catch the bug on the
g_en component. Correctly evaluate the log function present in the non-diagonal
tensor components when the shifted coordinate
xof the vertex is negative andit's equal to the negative of the distance
rbetween the vertex and thecomputation point. In that case the
log(x + r)can be replaced by-log(2|x|). Also, implement a modified version of the log function proposedby Fukushima (2020) for cases where the shifted coordinate of the node is
negative but different than the negative of the distance: improves the accuracy
when evaluating the log function on very small values. Now the
_safe_logfunction takes two arguments instead of one: the shifted coordinate
xand thedistance
r.