From 6a57561742833c2f1697219670214fa41e037884 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Tue, 24 Apr 2012 16:23:24 +0000
Subject: [PATCH] =?UTF-8?q?Neuer=20Test=20f=C3=BCr=20den=20Gradienten=20de?=
=?UTF-8?q?r=20Biegeenergy?=
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[[Imported from SVN: r8628]]
---
test/cosseratenergytest.cc | 160 +++++++++++++++++++++++++++++++++++--
1 file changed, 155 insertions(+), 5 deletions(-)
diff --git a/test/cosseratenergytest.cc b/test/cosseratenergytest.cc
index 27985cb3..068ec130 100644
--- a/test/cosseratenergytest.cc
+++ b/test/cosseratenergytest.cc
@@ -346,12 +346,14 @@ void testDerivativeOfGradientOfRotationMatrixWRTCoefficient(const LocalGeodesicF
// Evaluate the analytical derivative
Dune::array<Tensor3<double,3,3,4>, 3> dDR_dv;
+ Tensor3<double,3,domainDim,4> dDR3_dv;
CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3>::compute_dDR_dv(value,
derOfValueWRTx,
derOfValueWRTCoefficient,
derOfGradientWRTCoefficient,
- dDR_dv);
+ dDR_dv,
+ dDR3_dv);
Dune::array<Tensor3<double,3,3,4>, 3> dDR_dv_FD;
@@ -385,6 +387,153 @@ void testDerivativeOfGradientOfRotationMatrixWRTCoefficient(const LocalGeodesicF
}
+
+template <int domainDim, class GridType, class LocalFiniteElement>
+void testDerivativeOfBendingEnergy(const LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,RigidBodyMotion<double,3> >& f,
+ const FieldVector<double,domainDim>& local,
+ unsigned int coeff)
+{
+ ParameterTree materialParameters;
+ materialParameters["thickness"] = "1";
+ materialParameters["mu"] = "1";
+ materialParameters["lambda"] = "1";
+ materialParameters["mu_c"] = "1";
+ materialParameters["L_c"] = "1";
+ materialParameters["q"] = "1";
+ materialParameters["kappa"] = "1";
+
+ ConstantFunction<Dune::FieldVector<double,GridType::dimension>, Dune::FieldVector<double,3> > zeroFunction(Dune::FieldVector<double,3>(0));
+
+ CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3> assembler(materialParameters,
+ NULL,
+ &zeroFunction);
+
+
+ RigidBodyMotion<double,3> value = f.evaluate(local);
+ FieldMatrix<double,7,domainDim> derOfValueWRTx = f.evaluateDerivative(local);
+
+ FieldMatrix<double,7,7> derOfValueWRTCoefficient;
+ f.evaluateDerivativeOfValueWRTCoefficient(local, coeff, derOfValueWRTCoefficient);
+
+ Tensor3<double,7,7,domainDim> derOfGradientWRTCoefficient;
+ f.evaluateDerivativeOfGradientWRTCoefficient(local, coeff, derOfGradientWRTCoefficient);
+
+ Tensor3<double,7,7,domainDim> FDderOfGradientWRTCoefficient;
+ f.evaluateFDDerivativeOfGradientWRTCoefficient(local, coeff, FDderOfGradientWRTCoefficient);
+
+ // Evaluate the analytical derivative
+
+ Dune::array<Tensor3<double,3,3,4>, 3> dDR_dv;
+ Tensor3<double,3,domainDim,4> dDR3_dv;
+
+ CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3>::compute_dDR_dv(value,
+ derOfValueWRTx,
+ derOfValueWRTCoefficient,
+ derOfGradientWRTCoefficient,
+ dDR_dv,
+ dDR3_dv);
+
+ //
+ Dune::FieldMatrix<double,3,3> R;
+ value.q.matrix(R);
+
+ Tensor3<double,3,3,3> DR;
+ CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3>::computeDR(value, derOfValueWRTx, DR);
+
+ Tensor3<double,3,3,4> dR_dv;
+ CosseratEnergyLocalStiffness<typename GridType::LeafGridView,LocalFiniteElement,3>::computeDR_dv(value, derOfValueWRTCoefficient, dR_dv);
+
+ FieldVector<double,7> embeddedGradient;
+ assembler.bendingEnergyGradient(embeddedGradient,
+ R,
+ dR_dv,
+ DR,
+ dDR3_dv);
+
+
+ // ///////////////////////////////////////////////////////////
+ // Compute gradient by finite-difference approximation
+ // ///////////////////////////////////////////////////////////
+
+ double eps = 1e-4;
+ FieldVector<double,4> embeddedFDGradient;
+
+ size_t nDofs = f.localFiniteElement_.localBasis().size();
+ std::vector<TargetSpace> forwardSolution(nDofs);
+ std::vector<TargetSpace> backwardSolution(nDofs);
+
+ for (size_t i=0; i<nDofs; i++)
+ forwardSolution[i] = backwardSolution[i] = f.coefficient(i);
+
+ for (int j=0; j<4; j++) {
+
+ FieldVector<double,7> forwardCorrection(0);
+ forwardCorrection[j+3] += eps;
+
+ FieldVector<double,7> backwardCorrection(0);
+ backwardCorrection[j+3] -= eps;
+
+ forwardSolution[coeff] = TargetSpace(f.coefficient(coeff).globalCoordinates() + forwardCorrection);
+ backwardSolution[coeff] = TargetSpace(f.coefficient(coeff).globalCoordinates() + backwardCorrection);
+
+ LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,RigidBodyMotion<double,3> > forwardF(f.localFiniteElement_,forwardSolution);
+ LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,RigidBodyMotion<double,3> > backwardF(f.localFiniteElement_,backwardSolution);
+
+ RigidBodyMotion<double,3> forwardValue = forwardF.evaluate(local);
+ RigidBodyMotion<double,3> backwardValue = backwardF.evaluate(local);
+
+ FieldMatrix<double,3,3> forwardR, backwardR;
+ forwardValue.q.matrix(forwardR);
+ backwardValue.q.matrix(backwardR);
+
+ FieldMatrix<double,7,domainDim> forwardDerivative = forwardF.evaluateDerivative(local);
+ FieldMatrix<double,7,domainDim> backwardDerivative = backwardF.evaluateDerivative(local);
+
+ Tensor3<double,3,3,3> forwardDR;
+ Tensor3<double,3,3,3> backwardDR;
+
+ assembler.computeDR(forwardValue, forwardDerivative, forwardDR);
+ assembler.computeDR(backwardValue, backwardDerivative, backwardDR);
+
+ double forwardEnergy = assembler.bendingEnergy(forwardR, forwardDR);
+ double backwardEnergy = assembler.bendingEnergy(backwardR, backwardDR);
+
+ embeddedFDGradient[j] = (forwardEnergy - backwardEnergy) / (2*eps);
+
+ }
+
+ embeddedFDGradient = f.coefficient(coeff).q.projectOntoTangentSpace(embeddedFDGradient);
+
+ ////////////////////////////////////////////////
+ // Check whether the two are the same
+ ////////////////////////////////////////////////
+
+ double maxError = 0;
+ for (size_t i=0; i<4; i++) {
+ double diff = std::fabs(embeddedGradient[i+3] - embeddedFDGradient[i]);
+ maxError = std::max(maxError, diff);
+ }
+
+ if (maxError > 1e-3) {
+
+ std::cout << "Analytical and FD gradients differ!"
+ << " local: " << local
+ << " coefficient: " << coeff << std::endl;
+
+ std::cout << "embeddedGradient:" << std::endl;
+ std::cout << embeddedGradient[3] << " " << embeddedGradient[4] << " " << embeddedGradient[5] << " " << embeddedGradient[6] << std::endl << std::endl;
+
+ std::cout << "embeddedFDGradient:" << std::endl;
+ std::cout << embeddedFDGradient << std::endl;
+
+ abort();
+ }
+
+}
+
+
+
+
template <int domainDim>
void testDerivativeOfGradientOfRotationMatrixWRTCoefficient()
{
@@ -431,8 +580,11 @@ void testDerivativeOfGradientOfRotationMatrixWRTCoefficient()
= Dune::QuadratureRules<double, domainDim>::rule(GeometryType(GeometryType::simplex,domainDim), quadOrder);
for (size_t pt=0; pt<quad.size(); pt++) {
-
- testDerivativeOfGradientOfRotationMatrixWRTCoefficient<domainDim,GridType,LocalFiniteElement>(f, quad[pt].position(), j);
+
+ FieldVector<double,domainDim> quadPos = quad[pt].position();
+
+ testDerivativeOfGradientOfRotationMatrixWRTCoefficient<domainDim,GridType,LocalFiniteElement>(f, quadPos, j);
+ testDerivativeOfBendingEnergy<domainDim,GridType,LocalFiniteElement>(f, quadPos, j);
}
@@ -463,8 +615,6 @@ void testEnergyGradient()
PQkLocalFiniteElementCache<double,double,GridType::dimension,1> feCache;
typedef typename PQkLocalFiniteElementCache<double,double,GridType::dimension,1>::FiniteElementType LocalFiniteElement;
- //LocalGeodesicFEFunction<domainDim,double,LocalFiniteElement,TargetSpace> f(feCache.get(element),corners);
-
ParameterTree materialParameters;
materialParameters["thickness"] = "0.1";
materialParameters["mu"] = "3.8462e+05";
--
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