From a4e6774e8fe9f77ec96a538e91cbaaf6c3420363 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Tue, 31 Aug 2010 13:20:41 +0000
Subject: [PATCH] implement the third derivative of arccos squared
[[Imported from SVN: r6296]]
---
dune/gfe/unitvector.hh | 13 +++++++++++++
1 file changed, 13 insertions(+)
diff --git a/dune/gfe/unitvector.hh b/dune/gfe/unitvector.hh
index f25332f6c..28d4ef49a 100644
--- a/dune/gfe/unitvector.hh
+++ b/dune/gfe/unitvector.hh
@@ -34,6 +34,19 @@ class UnitVector
return 2/(1-x*x) - 2*x*std::acos(x) / std::pow(1-x*x,1.5);
}
+ /** \brief Compute the third derivative of arccos^2 without getting unstable for x close to 1 */
+ static double thirdDerivativeOfArcCosSquared(const double& x) {
+ const double eps = 1e-12;
+ if (x > 1-eps) { // regular expression is unstable, use the series expansion instead
+ return -8.0/15 + 24*(x-1)/35;
+ } else if (x < -1+eps) { // The function is not differentiable
+ DUNE_THROW(Dune::Exception, "arccos^2 is not differentiable at x==-1!");
+ } else {
+ double d = 1-x*x;
+ return 6*x/(d*d) - 6*x*x*std::acos(x)/(d*d*std::sqrt(d)) - 2*std::acos(x)/(d*std::sqrt(d));
+ }
+ }
+
public:
/** \brief The type used for coordinates */
--
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