From 30a34d27746e02c338b3720a6022f514f4ac596b Mon Sep 17 00:00:00 2001
From: Oliver Sander <oliver.sander@tu-dresden.de>
Date: Mon, 8 Feb 2016 13:09:05 +0100
Subject: [PATCH] Weight the integral with the norm of the derivative of the
previous time step
According to Hanne, this is needed to turn 1d harmonic map heat flow into true
curve-shortening flow.
Hardwiring the weighting here is very hacky. Something more flexible and
general will need to be implemented eventually.
---
dune/gfe/l2distancesquaredenergy.hh | 19 ++++++++++++++++++-
1 file changed, 18 insertions(+), 1 deletion(-)
diff --git a/dune/gfe/l2distancesquaredenergy.hh b/dune/gfe/l2distancesquaredenergy.hh
index d08571cd..1307fe0d 100644
--- a/dune/gfe/l2distancesquaredenergy.hh
+++ b/dune/gfe/l2distancesquaredenergy.hh
@@ -57,8 +57,25 @@ public:
UnitVector<double,3> originValue;
origin_->evaluateLocal(element,quadPos, originValue);
+ // The derivative of the 'origin' function
+ // First: as function defined on the reference element
+ typename VirtualGridViewFunction<GridView,UnitVector<double,3> >::DerivativeType originReferenceDerivative;
+ origin_->evaluateDerivativeLocal(element,quadPos,originReferenceDerivative);
+
+ // The derivative of the function defined on the actual element
+ typename VirtualGridViewFunction<GridView,UnitVector<double,3> >::DerivativeType originDerivative(0);
+
+ auto jacobianInverseTransposed = element.geometry().jacobianInverseTransposed(quadPos);
+
+ for (size_t comp=0; comp<originReferenceDerivative.N(); comp++)
+ jacobianInverseTransposed.umv(originReferenceDerivative[comp], originDerivative[comp]);
+
+ double weightFactor = originDerivative.frobenius_norm();
+ // un-comment the following line to switch off the weight factor
+ //weightFactor = 1.0;
+
// Add the local energy density
- energy += weight * TargetSpace::distanceSquared(originValue, value);
+ energy += weight * weightFactor * TargetSpace::distanceSquared(originValue, value);
}
--
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