From c5da8b9f8a7af7f8d3c933e16171d14c319ce903 Mon Sep 17 00:00:00 2001
From: Jonathan Youett <youett@math.fu-berlin.de>
Date: Fri, 31 Oct 2014 14:50:20 +0100
Subject: [PATCH] Add test for the automatic differentiation assemblers
comparing them to local assemblers of a nonlinear elasticity functional,
derived by hand.
---
dune/fufem/test/CMakeLists.txt | 5 +-
dune/fufem/test/Makefile.am | 6 +
dune/fufem/test/adolctest.cc | 290 ++++++++++++
dune/fufem/test/adolctest.sol | 833 +++++++++++++++++++++++++++++++++
4 files changed, 1133 insertions(+), 1 deletion(-)
create mode 100644 dune/fufem/test/adolctest.cc
create mode 100644 dune/fufem/test/adolctest.sol
diff --git a/dune/fufem/test/CMakeLists.txt b/dune/fufem/test/CMakeLists.txt
index f95c222b..7d764132 100644
--- a/dune/fufem/test/CMakeLists.txt
+++ b/dune/fufem/test/CMakeLists.txt
@@ -1,5 +1,6 @@
# Put your test in here if it needs access to external grids
set(GRID_BASED_TESTS
+ adolctest
basisgridfunctiontest
basisinterpolatortest
boundarypatchtest
@@ -66,7 +67,9 @@ if(PYTHONLIBS_FOUND)
target_compile_definitions(dunepythontest PRIVATE -DDUNE_FUFEM_TEST_MODULE_PATH=\"${CMAKE_CURRENT_BINARY_DIR}\")
endif()
-
+if (ADOLC_FOUND)
+ add_dune_adolc_flags(adolctest)
+endif()
add_directory_test_target(_test_target)
diff --git a/dune/fufem/test/Makefile.am b/dune/fufem/test/Makefile.am
index 074f60d8..9f29d906 100644
--- a/dune/fufem/test/Makefile.am
+++ b/dune/fufem/test/Makefile.am
@@ -1,6 +1,7 @@
# list of tests to run
TESTS = arithmetictest\
+ adolctest \
basisgridfunctiontest \
basisinterpolatortest \
boundarypatchtest \
@@ -48,6 +49,11 @@ arithmetictest_CPPFLAGS = $(COMMON_CPPFLAGS)
arithmetictest_LDADD = $(COMMON_LDADD)
arithmetictest_LDFLAGS = $(COMMON_LDFLAGS)
+adolctest_SOURCES = adolctest.cc
+adolctest_CPPFLAGS = $(COMMON_CPPFLAGS) $(GRID_CPPFLAGS) $(ADOLC_CPPFLAGS)
+adolctest_LDADD = $(COMMON_LDADD) $(GRID_LDADD) $(ADOLC_LDFLAGS)
+adolctest_LDFLAGS = $(COMMON_LDFLAGS) $(GRID_LDFLAGS) $(ADOLC_LDFLAGS)
+
basisgridfunctiontest_SOURCES = basisgridfunctiontest.cc
basisgridfunctiontest_CPPFLAGS = $(COMMON_CPPFLAGS) $(GRID_CPPFLAGS)
basisgridfunctiontest_LDADD = $(COMMON_LDADD) $(GRID_LDADD)
diff --git a/dune/fufem/test/adolctest.cc b/dune/fufem/test/adolctest.cc
new file mode 100644
index 00000000..d1c664a3
--- /dev/null
+++ b/dune/fufem/test/adolctest.cc
@@ -0,0 +1,290 @@
+#include <config.h>
+#include <fstream>
+
+#include <dune/common/fmatrix.hh>
+#include <dune/common/fvector.hh>
+#include <dune/common/timer.hh>
+
+#include <dune/grid/uggrid.hh>
+//#include <dune/grid/io/file/dgfparser/gridptr.hh>
+//#include <dune/grid/io/file/dgfparser/dgfug.hh>
+
+#include <dune/istl/io.hh>
+#include <dune/istl/bcrsmatrix.hh>
+
+#include <dune/fufem/assemblers/localassemblers/adolclocalenergy.hh>
+#include <dune/fufem/assemblers/localassemblers/adolclinearizationassembler.hh>
+#include <dune/fufem/assemblers/localassemblers/adolchessianassembler.hh>
+#include <dune/fufem/functionspacebases/p1nodalbasis.hh>
+#include <dune/fufem/functions/basisgridfunction.hh>
+#include <dune/fufem/assemblers/functionalassembler.hh>
+#include <dune/fufem/assemblers/operatorassembler.hh>
+#include <dune/fufem/assemblers/localassemblers/geomexactstvenantkirchhofffunctionalassembler.hh>
+#include <dune/fufem/assemblers/localassemblers/geomexactstvenantkirchhoffoperatorassembler.hh>
+#include <dune/fufem/quadraturerules/quadraturerulecache.hh>
+#include <dune/fufem/symmetrictensor.hh>
+#include <dune/fufem/makesphere.hh>
+
+
+//! Local energy for a geometric exact St. Venant--Kirchhoff material
+template <class GridType, class LocalFiniteElement>
+class LocalElasticity : public Adolc::LocalEnergy<GridType, LocalFiniteElement,GridType::dimension>
+{
+ public:
+
+ enum {dim = GridType::dimension};
+ typedef typename GridType::ctype ctype;
+ typedef typename LocalFiniteElement::Traits::LocalBasisType::Traits::RangeFieldType field_type;
+
+ typedef Adolc::LocalEnergy<GridType, LocalFiniteElement, dim> Base;
+ typedef typename Base::CoefficientVectorType CoefficientVectorType;
+ typedef typename Base::ReturnType ReturnType;
+
+ typedef typename GridType::template Codim<0>::Entity Element;
+ typedef typename LocalFiniteElement::Traits::LocalBasisType::Traits::JacobianType JacobianType;
+
+ LocalElasticity(field_type E, field_type nu) : E_(E), nu_(nu) {}
+
+ ReturnType energy(const Element& element, const LocalFiniteElement& lfe,
+ const CoefficientVectorType& localCoeff) const
+ {
+ ReturnType energy(0);
+
+ // get quadrature rule
+ QuadratureRuleKey quad1(lfe);
+ QuadratureRuleKey quadKey = quad1.derivative().square().square();
+
+ const Dune::QuadratureRule<ctype, dim>& quad = QuadratureRuleCache<ctype, dim>::rule(quadKey);
+
+ // store gradients of shape functions and base functions
+ std::vector<JacobianType> referenceGradients(lfe.localBasis().size());
+
+ // the element geometry mapping
+ const typename Element::Geometry geometry = element.geometry();
+
+ // loop over quadrature points
+ for (size_t pt=0; pt < quad.size(); ++pt) {
+
+ // get quadrature point
+ const auto& quadPos = quad[pt].position();
+
+ // evaluate displacement gradient at the quadrature point
+
+ // get transposed inverse of Jacobian of transformation
+ const auto& invJacobian = geometry.jacobianInverseTransposed(quadPos);
+
+ // get integration factor
+ const ctype integrationElement = geometry.integrationElement(quadPos);
+
+ // get gradients of shape functions
+ lfe.localBasis().evaluateJacobian(quadPos, referenceGradients);
+
+ // compute gradient of the configuration
+ Dune::FieldMatrix<ReturnType,dim,dim> localGradient(0);
+ for (size_t k=0; k<referenceGradients.size(); ++k) {
+ Dune::FieldVector<ReturnType,dim> gradient(0);
+ invJacobian.umv(referenceGradients[k][0], gradient);
+ for (int i=0; i<dim; ++i)
+ for (int j=0; j<dim; ++j)
+ localGradient[i][j] += localCoeff[k][i] * gradient[j];
+ }
+
+ // Compute the nonlinear strain tensor from the deformation gradient
+ SymmetricTensor<dim,ReturnType> strain(0),stress(0);
+
+ computeNonlinearStrain(localGradient,strain);
+
+ // and the stress
+ stress = hookeTimesStrain(strain);
+
+ ReturnType z = quad[pt].weight()*integrationElement;
+ energy += (stress*strain)*z;
+ }
+
+ return 0.5*energy;
+ }
+
+ private:
+ /** \brief Compute nonlinear strain tensor from a displacement gradient.
+ *
+ * \param grad The gradient of the direction in which the linearisation is computed.
+ * \param strain The tensor to store the strain in.
+ */
+ static void computeNonlinearStrain(const Dune::FieldMatrix<ReturnType, dim, dim>& grad,
+ SymmetricTensor<dim, ReturnType>& strain) {
+ strain = ReturnType(0);
+ for (int i=0; i<dim ; ++i) {
+ strain(i,i) +=grad[i][i];
+
+ for (int k=0;k<dim;++k)
+ strain(i,i) += 0.5*grad[k][i]*grad[k][i];
+
+ for (int j=i+1; j<dim; ++j) {
+ strain(i,j) += 0.5*(grad[i][j] + grad[j][i]);
+ for (int k=0;k<dim;++k)
+ strain(i,j) += 0.5*grad[k][i]*grad[k][j];
+ }
+ }
+ }
+
+ //! Compute linear elastic stress from the strain
+ SymmetricTensor<dim,ReturnType> hookeTimesStrain(const SymmetricTensor<dim,ReturnType>& strain) const {
+
+ SymmetricTensor<dim,ReturnType> stress = strain;
+ stress *= E_/(1+nu_);
+
+ ReturnType f = E_*nu_ / ((1+nu_)*(1-2*nu_)) * strain.trace();
+ stress.addToDiag(f);
+
+ return stress;
+ }
+
+ field_type E_;
+ field_type nu_;
+
+};
+
+
+// grid dimension
+const int dim = 3;
+
+using namespace Dune;
+int main (int argc, char *argv[]) try
+{
+
+ typedef FieldVector<double,dim> FVector;
+ typedef FieldMatrix<double,dim,dim> FMatrix;
+ typedef BlockVector<FVector> VectorType;
+ typedef BCRSMatrix<FMatrix> MatrixType;
+ typedef std::vector<FVector> CoeffType;
+
+ // ///////////////////////////////////////
+ // Create the grid
+ // ///////////////////////////////////////
+
+ typedef UGGrid<dim> GridType;
+ GridType* grid = new GridType;
+ makeSphere(*grid,FVector(0),0.2);
+ grid->globalRefine(3);
+ typedef GridType::LeafGridView GridView;
+ GridView gridView = grid->leafGridView();
+
+ typedef P1NodalBasis<GridView> FEBasis;
+ FEBasis feBasis(gridView);
+
+ // //////////////////////////
+ // Initial iterate
+ // //////////////////////////
+
+ std::ifstream infile("adolctest.sol");
+ std::string line;
+
+ VectorType x(feBasis.size());
+ int i=0;
+ while (std::getline(infile, line))
+ {
+ std::istringstream iss(line);
+ for (int j=0; j<dim;j++)
+ iss >> x[i][j];
+ i++;
+ }
+
+ auto xGridFunc = make_shared<BasisGridFunction<FEBasis,VectorType> >(feBasis,x);
+
+ // ////////////////////////////////////////////////////////////
+ // Create an assembler for the energy functional
+ // ////////////////////////////////////////////////////////////
+
+ double E = 1e5;
+ double nu = 0.4;
+
+ typedef FEBasis::LocalFiniteElement Lfe;
+ LocalElasticity<GridType,Lfe> localEnergy(E,nu);
+ AdolcLinearizationAssembler<GridType,Lfe,FVector> linAdolcAssembler(localEnergy,*xGridFunc);
+
+ GeomExactStVenantKirchhoffFunctionalAssembler<GridType, Lfe> linPaperAssembler(E,nu);
+ linPaperAssembler.setConfiguration(xGridFunc);
+
+ FunctionalAssembler<FEBasis> functionalAssembler(feBasis);
+
+ VectorType adolcGradient(feBasis.size());
+ VectorType paperGrad(feBasis.size());
+
+ adolcGradient = 0;
+ paperGrad = 0;
+
+ Dune::Timer time;
+ functionalAssembler.assemble(linAdolcAssembler,adolcGradient);
+ std::cout<<"ADOL-C functional assembler needed "<<time.stop()<<std::endl;
+
+ time.reset();
+ time.start();
+ functionalAssembler.assemble(linPaperAssembler,paperGrad);
+ std::cout<<"Paper&Pen functional assembler needed "<<time.stop()<<std::endl;
+
+ for (size_t i=0; i<adolcGradient.size();i++) {
+
+ FVector diff = adolcGradient[i];
+ diff -= paperGrad[i];
+
+ if (diff.two_norm()>1e-9)
+ DUNE_THROW(Dune::Exception,"Wrong local derivative, error is "<<diff.two_norm());
+
+ }
+ // ////////////////////////
+ // Test hessian assembler
+ // ////////////////////////
+
+ AdolcHessianAssembler<GridType,Lfe,Lfe,FMatrix> hessAdolcAssembler(localEnergy,*xGridFunc);
+ GeomExactStVenantKirchhoffOperatorAssembler<GridType, Lfe,Lfe> hessPaperAssembler(E,nu);
+
+ hessPaperAssembler.setConfiguration(xGridFunc);
+
+ OperatorAssembler<FEBasis,FEBasis> operatorAssembler(feBasis,feBasis);
+
+ MatrixType adolcHessian, paperHessian;
+
+ time.reset();
+ time.start();
+ operatorAssembler.assemble(hessAdolcAssembler, adolcHessian);
+ std::cout<<"ADOL-C operator assembler needed "<<time.stop()<<std::endl;
+
+ time.reset();
+ time.start();
+
+ operatorAssembler.assemble(hessPaperAssembler, paperHessian);
+ std::cout<<"Paper&Pen operator assembler needed "<<time.stop()<<std::endl;
+
+ for (size_t i=0; i<adolcHessian.N();i++) {
+
+ const auto& adolcRow = adolcHessian[i];
+ const auto& paperRow = paperHessian[i];
+
+ auto adolcIt = adolcRow.begin();
+ auto adolcEndIt = adolcRow.end();
+
+ auto paperIt = paperRow.begin();
+ auto paperEndIt = paperRow.end();
+
+ for (; adolcIt != adolcEndIt; ++adolcIt, ++paperIt) {
+
+ if (adolcIt.index() != paperIt.index())
+ DUNE_THROW(Dune::Exception,"Not the same sparsity pattern!"<<adolcIt.index()
+ <<"!="<<paperIt.index());
+
+ FMatrix diff = *adolcIt;
+ diff -= *paperIt;
+
+ if (diff.frobenius_norm()>1e-8)
+ DUNE_THROW(Dune::Exception,"Wrong local hessian, error is "<<diff.frobenius_norm());
+
+ }
+ assert(paperIt==paperEndIt);
+ }
+
+ // //////////////////////////////
+} catch (Exception e) {
+
+ std::cout << e << std::endl;
+
+}
diff --git a/dune/fufem/test/adolctest.sol b/dune/fufem/test/adolctest.sol
new file mode 100644
index 00000000..288ca126
--- /dev/null
+++ b/dune/fufem/test/adolctest.sol
@@ -0,0 +1,833 @@
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--
GitLab