Skip to content
Snippets Groups Projects

Compare revisions

Changes are shown as if the source revision was being merged into the target revision. Learn more about comparing revisions.

Source

Select target project
No results found

Target

Select target project
  • podlesny/dune-tectonic
  • agnumpde/dune-tectonic
2 results
Show changes
Showing
with 52 additions and 567 deletions
#ifndef SRC_HDF5_WRITER_HH
#define SRC_HDF5_WRITER_HH
#include <dune/fufem/functions/basisgridfunction.hh>
#include <dune/fufem/geometry/convexpolyhedron.hh>
#include <dune/fufem/hdf5/file.hh>
#include "hdf5/frictionalboundary-writer.hh"
#include "hdf5/iteration-writer.hh"
#include "hdf5/patchinfo-writer.hh"
#include "hdf5/surface-writer.hh"
#include "hdf5/time-writer.hh"
template <class ProgramState, class VertexBasis, class GridView>
class HDF5Writer {
private:
using Vector = typename ProgramState::Vector;
using Patch = BoundaryPatch<GridView>;
using LocalVector = typename Vector::block_type;
public:
HDF5Writer(HDF5::Grouplike &file, Vector const &vertexCoordinates,
VertexBasis const &vertexBasis, Patch const &surface,
Patch const &frictionalBoundary,
ConvexPolyhedron<LocalVector> const &weakPatch)
: file_(file),
iterationWriter_(file_),
timeWriter_(file_),
#if MY_DIM == 3
patchInfoWriter_(file_, vertexBasis, frictionalBoundary, weakPatch),
#endif
surfaceWriter_(file_, vertexCoordinates, surface),
frictionalBoundaryWriter_(file_, vertexCoordinates,
frictionalBoundary) {
}
template <class Friction>
void reportSolution(ProgramState const &programState,
// for the friction coefficient
Friction &friction) {
timeWriter_.write(programState);
#if MY_DIM == 3
patchInfoWriter_.write(programState);
#endif
surfaceWriter_.write(programState);
frictionalBoundaryWriter_.write(programState, friction);
}
void reportIterations(ProgramState const &programState,
IterationRegister const &iterationCount) {
iterationWriter_.write(programState.timeStep, iterationCount);
}
private:
HDF5::Grouplike &file_;
IterationWriter iterationWriter_;
TimeWriter<ProgramState> timeWriter_;
#if MY_DIM == 3
PatchInfoWriter<ProgramState, VertexBasis, GridView> patchInfoWriter_;
#endif
SurfaceWriter<ProgramState, GridView> surfaceWriter_;
FrictionalBoundaryWriter<ProgramState, GridView> frictionalBoundaryWriter_;
};
#endif
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <dune/fufem/hdf5/singletonwriter.hh>
#include "frictionalboundary-writer.hh"
#include "restrict.hh"
template <class ProgramState, class GridView>
FrictionalBoundaryWriter<ProgramState, GridView>::FrictionalBoundaryWriter(
HDF5::Grouplike &file, Vector const &vertexCoordinates,
Patch const &frictionalBoundary)
: group_(file, "frictionalBoundary"),
frictionalBoundary_(frictionalBoundary),
frictionalBoundaryDisplacementWriter_(group_, "displacement",
frictionalBoundary.numVertices(),
Vector::block_type::dimension),
frictionalBoundaryVelocityWriter_(group_, "velocity",
frictionalBoundary.numVertices(),
Vector::block_type::dimension),
frictionalBoundaryStateWriter_(group_, "state",
frictionalBoundary.numVertices()),
frictionalBoundaryCoefficientWriter_(group_, "coefficient",
frictionalBoundary.numVertices()) {
auto const frictionalBoundaryCoordinates =
restrictToSurface(vertexCoordinates, frictionalBoundary);
HDF5::SingletonWriter<2> frictionalBoundaryCoordinateWriter(
group_, "coordinates", frictionalBoundaryCoordinates.size(),
Vector::block_type::dimension);
setEntry(frictionalBoundaryCoordinateWriter, frictionalBoundaryCoordinates);
}
template <class ProgramState, class GridView>
template <class Friction>
void FrictionalBoundaryWriter<ProgramState, GridView>::write(
ProgramState const &programState, Friction &friction) {
auto const frictionalBoundaryDisplacements =
restrictToSurface(programState.u, frictionalBoundary_);
addEntry(frictionalBoundaryDisplacementWriter_, programState.timeStep,
frictionalBoundaryDisplacements);
auto const frictionalBoundaryVelocities =
restrictToSurface(programState.v, frictionalBoundary_);
addEntry(frictionalBoundaryVelocityWriter_, programState.timeStep,
frictionalBoundaryVelocities);
auto const frictionalBoundaryStates =
restrictToSurface(programState.alpha, frictionalBoundary_);
addEntry(frictionalBoundaryStateWriter_, programState.timeStep,
frictionalBoundaryStates);
friction.updateAlpha(programState.alpha);
auto const c = friction.coefficientOfFriction(programState.v);
auto const frictionalBoundaryCoefficient =
restrictToSurface(c, frictionalBoundary_);
addEntry(frictionalBoundaryCoefficientWriter_, programState.timeStep,
frictionalBoundaryCoefficient);
}
#include "frictionalboundary-writer_tmpl.cc"
#ifndef SRC_HDF_FRICTIONALBOUNDARY_WRITER_HH
#define SRC_HDF_FRICTIONALBOUNDARY_WRITER_HH
#include <dune/fufem/boundarypatch.hh>
#include <dune/fufem/hdf5/sequenceio.hh>
template <class ProgramState, class GridView> class FrictionalBoundaryWriter {
using ScalarVector = typename ProgramState::ScalarVector;
using Vector = typename ProgramState::Vector;
using Patch = BoundaryPatch<GridView>;
public:
FrictionalBoundaryWriter(HDF5::Grouplike &file, Vector const &vertexCoordinates,
Patch const &frictionalBoundary);
template <class Friction>
void write(ProgramState const &programState, Friction &friction);
private:
HDF5::Group group_;
Patch const &frictionalBoundary_;
HDF5::SequenceIO<2> frictionalBoundaryDisplacementWriter_;
HDF5::SequenceIO<2> frictionalBoundaryVelocityWriter_;
HDF5::SequenceIO<1> frictionalBoundaryStateWriter_;
HDF5::SequenceIO<1> frictionalBoundaryCoefficientWriter_;
};
#endif
#include "../explicitvectors.hh"
#include "../explicitgrid.hh"
#include "../program_state.hh"
using MyProgramState = ProgramState<Vector, ScalarVector>;
using MyFriction = GlobalFriction<Matrix, Vector>;
template class FrictionalBoundaryWriter<MyProgramState, GridView>;
template void FrictionalBoundaryWriter<MyProgramState, GridView>::write(
MyProgramState const &programState, MyFriction &friction);
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "iteration-writer.hh"
IterationWriter::IterationWriter(HDF5::Grouplike &file)
: group_(file, "iterations"),
fpiSubGroup_(group_, "fixedPoint"),
mgSubGroup_(group_, "multiGrid"),
finalMGIterationWriter_(mgSubGroup_, "final"),
finalFPIIterationWriter_(fpiSubGroup_, "final"),
totalMGIterationWriter_(mgSubGroup_, "total"),
totalFPIIterationWriter_(fpiSubGroup_, "total") {}
void IterationWriter::write(size_t timeStep,
IterationRegister const &iterationCount) {
addEntry(finalMGIterationWriter_, timeStep,
iterationCount.finalCount.multigridIterations);
addEntry(finalFPIIterationWriter_, timeStep,
iterationCount.finalCount.iterations);
addEntry(totalMGIterationWriter_, timeStep,
iterationCount.totalCount.multigridIterations);
addEntry(totalFPIIterationWriter_, timeStep,
iterationCount.totalCount.iterations);
}
#ifndef SRC_HDF_ITERATION_WRITER_HH
#define SRC_HDF_ITERATION_WRITER_HH
#include <dune/fufem/hdf5/sequenceio.hh>
#include "../time-stepping/adaptivetimestepper.hh"
class IterationWriter {
public:
IterationWriter(HDF5::Grouplike &file);
void write(size_t timeStep, IterationRegister const &iterationCount);
private:
HDF5::Group group_;
HDF5::Group fpiSubGroup_;
HDF5::Group mgSubGroup_;
HDF5::SequenceIO<0, size_t> finalMGIterationWriter_;
HDF5::SequenceIO<0, size_t> finalFPIIterationWriter_;
HDF5::SequenceIO<0, size_t> totalMGIterationWriter_;
HDF5::SequenceIO<0, size_t> totalFPIIterationWriter_;
};
#endif
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <dune/fufem/grid/hierarchic-approximation.hh>
#include <dune/fufem/hdf5/singletonwriter.hh>
#include "patchinfo-writer.hh"
template <class LocalVector, class GridView>
GridEvaluator<LocalVector, GridView>::GridEvaluator(
ConvexPolyhedron<LocalVector> const &weakPatch, GridView const &gridView) {
double const bufferWidth = 0.05 * MyGeometry::lengthScale;
auto const xminmax = std::minmax_element(
weakPatch.vertices.begin(), weakPatch.vertices.end(),
[](LocalVector const &a, LocalVector const &b) { return a[0] < b[0]; });
double const xmin = (*xminmax.first)[0] - bufferWidth;
double const xspan = (*xminmax.second)[0] + bufferWidth - xmin;
double const zmin = -MyGeometry::depth / 2.0;
double const zspan = MyGeometry::depth;
double spatialResolution = 0.01 * MyGeometry::lengthScale;
size_t const xsteps = std::round(xspan / spatialResolution);
size_t const zsteps = std::round(zspan / spatialResolution);
xCoordinates.resize(xsteps + 1);
for (size_t xi = 0; xi <= xsteps; xi++)
xCoordinates[xi] = xmin + xi * xspan / xsteps;
zCoordinates.resize(zsteps + 1);
for (size_t zi = 0; zi <= zsteps; zi++)
zCoordinates[zi] = zmin + zi * zspan / zsteps;
HierarchicApproximation<typename GridView::Grid, GridView> const
hApproximation(gridView.grid(), gridView, 1e-6 * MyGeometry::lengthScale);
LocalVector global(0);
localInfo.resize(xsteps + 1);
for (size_t xi = 0; xi < xCoordinates.size(); ++xi) {
localInfo[xi].resize(zsteps + 1);
for (size_t zi = 0; zi < zCoordinates.size(); ++zi) {
global[0] = xCoordinates[xi];
global[2] = zCoordinates[zi];
auto const element = hApproximation.findEntity(global);
localInfo[xi][zi] =
std::make_pair(element, element.geometry().local(global));
}
}
}
template <class LocalVector, class GridView>
template <class Function>
Dune::Matrix<typename Function::RangeType>
GridEvaluator<LocalVector, GridView>::evaluate(Function const &f) const {
Dune::Matrix<typename Function::RangeType> ret(xCoordinates.size(),
zCoordinates.size());
for (size_t xi = 0; xi < localInfo.size(); ++xi) {
auto const &localInfoX = localInfo[xi];
for (size_t zi = 0; zi < localInfoX.size(); ++zi) {
auto const &localInfoXZ = localInfoX[zi];
f.evaluateLocal(localInfoXZ.first, localInfoXZ.second, ret[xi][zi]);
}
}
return ret;
}
template <class ProgramState, class VertexBasis, class GridView>
PatchInfoWriter<ProgramState, VertexBasis, GridView>::PatchInfoWriter(
HDF5::Grouplike &file, VertexBasis const &vertexBasis,
Patch const &frictionalBoundary,
ConvexPolyhedron<LocalVector> const &weakPatch)
: group_(file, "weakPatchGrid"),
vertexBasis_(vertexBasis),
gridEvaluator_(weakPatch, frictionalBoundary.gridView()),
weakPatchGridVelocityWriter_(
group_, "velocity", gridEvaluator_.xCoordinates.size(),
gridEvaluator_.zCoordinates.size(), Vector::block_type::dimension) {
HDF5::SingletonWriter<1> weakPatchGridXCoordinateWriter(
group_, "xCoordinates", gridEvaluator_.xCoordinates.size());
setEntry(weakPatchGridXCoordinateWriter, gridEvaluator_.xCoordinates);
HDF5::SingletonWriter<1> weakPatchGridZCoordinateWriter(
group_, "zCoordinates", gridEvaluator_.zCoordinates.size());
setEntry(weakPatchGridZCoordinateWriter, gridEvaluator_.zCoordinates);
}
template <class ProgramState, class VertexBasis, class GridView>
void PatchInfoWriter<ProgramState, VertexBasis, GridView>::write(
ProgramState const &programState) {
BasisGridFunction<VertexBasis, Vector> velocity(vertexBasis_, programState.v);
auto const gridVelocity = gridEvaluator_.evaluate(velocity);
addEntry(weakPatchGridVelocityWriter_, programState.timeStep, gridVelocity);
}
#include "patchinfo-writer_tmpl.cc"
#ifndef SRC_HDF_PATCHINFO_WRITER_HH
#define SRC_HDF_PATCHINFO_WRITER_HH
#include <dune/istl/matrix.hh>
#include <dune/fufem/boundarypatch.hh>
#include <dune/fufem/functions/basisgridfunction.hh>
#include <dune/fufem/geometry/convexpolyhedron.hh>
#include <dune/fufem/hdf5/sequenceio.hh>
#include "../one-body-problem-data/mygeometry.hh"
template <class LocalVector, class GridView> class GridEvaluator {
using Element = typename GridView::Grid::template Codim<0>::Entity;
public:
GridEvaluator(ConvexPolyhedron<LocalVector> const &weakPatch,
GridView const &gridView);
template <class Function>
Dune::Matrix<typename Function::RangeType> evaluate(Function const &f) const;
Dune::BlockVector<Dune::FieldVector<double, 1>> xCoordinates;
Dune::BlockVector<Dune::FieldVector<double, 1>> zCoordinates;
private:
std::vector<std::vector<std::pair<Element, LocalVector>>> localInfo;
};
template <class ProgramState, class VertexBasis, class GridView>
class PatchInfoWriter {
using Vector = typename ProgramState::Vector;
using LocalVector = typename Vector::block_type;
using Patch = BoundaryPatch<GridView>;
public:
PatchInfoWriter(HDF5::Grouplike &file, VertexBasis const &vertexBasis,
Patch const &frictionalBoundary,
ConvexPolyhedron<LocalVector> const &weakPatch);
void write(ProgramState const &programState);
private:
HDF5::Group group_;
VertexBasis const &vertexBasis_;
GridEvaluator<LocalVector, GridView> const gridEvaluator_;
HDF5::SequenceIO<3> weakPatchGridVelocityWriter_;
};
#endif
#include "../explicitvectors.hh"
#include "../explicitgrid.hh"
#include "../program_state.hh"
using MyProgramState = ProgramState<Vector, ScalarVector>;
using P1Basis = P1NodalBasis<GridView, double>;
using MyFunction = BasisGridFunction<P1Basis, Vector>;
template class GridEvaluator<LocalVector, GridView>;
template Dune::Matrix<typename MyFunction::RangeType>
GridEvaluator<LocalVector, GridView>::evaluate(MyFunction const &f) const;
template class PatchInfoWriter<MyProgramState, P1Basis, GridView>;
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "restart-io.hh"
template <class ProgramState>
RestartIO<ProgramState>::RestartIO(HDF5::Grouplike &group, size_t vertexCount)
: displacementWriter_(group, "displacement", vertexCount,
Vector::block_type::dimension),
velocityWriter_(group, "velocity", vertexCount,
Vector::block_type::dimension),
accelerationWriter_(group, "acceleration", vertexCount,
Vector::block_type::dimension),
stateWriter_(group, "state", vertexCount),
weightedNormalStressWriter_(group, "weightedNormalStress", vertexCount),
relativeTimeWriter_(group, "relativeTime"),
relativeTimeIncrementWriter_(group, "relativeTimeIncrement") {}
template <class ProgramState>
void RestartIO<ProgramState>::write(ProgramState const &programState) {
addEntry(displacementWriter_, programState.timeStep, programState.u);
addEntry(velocityWriter_, programState.timeStep, programState.v);
addEntry(accelerationWriter_, programState.timeStep, programState.a);
addEntry(stateWriter_, programState.timeStep, programState.alpha);
addEntry(weightedNormalStressWriter_, programState.timeStep,
programState.weightedNormalStress);
addEntry(relativeTimeWriter_, programState.timeStep,
programState.relativeTime);
addEntry(relativeTimeIncrementWriter_, programState.timeStep,
programState.relativeTau);
}
template <class ProgramState>
void RestartIO<ProgramState>::read(size_t timeStep,
ProgramState &programState) {
programState.timeStep = timeStep;
readEntry(displacementWriter_, timeStep, programState.u);
readEntry(velocityWriter_, timeStep, programState.v);
readEntry(accelerationWriter_, timeStep, programState.a);
readEntry(stateWriter_, timeStep, programState.alpha);
readEntry(weightedNormalStressWriter_, timeStep,
programState.weightedNormalStress);
readEntry(relativeTimeWriter_, timeStep, programState.relativeTime);
readEntry(relativeTimeIncrementWriter_, timeStep, programState.relativeTau);
}
#include "restart-io_tmpl.cc"
#ifndef SRC_HDF_RESTART_HDF_HH
#define SRC_HDF_RESTART_HDF_HH
#include <dune/fufem/hdf5/file.hh>
#include <dune/fufem/hdf5/sequenceio.hh>
template <class ProgramState> class RestartIO {
using ScalarVector = typename ProgramState::ScalarVector;
using Vector = typename ProgramState::Vector;
public:
RestartIO(HDF5::Grouplike &group, size_t vertexCount);
void write(ProgramState const &programState);
void read(size_t timeStep, ProgramState &programState);
private:
HDF5::SequenceIO<2> displacementWriter_;
HDF5::SequenceIO<2> velocityWriter_;
HDF5::SequenceIO<2> accelerationWriter_;
HDF5::SequenceIO<1> stateWriter_;
HDF5::SequenceIO<1> weightedNormalStressWriter_;
HDF5::SequenceIO<0> relativeTimeWriter_;
HDF5::SequenceIO<0> relativeTimeIncrementWriter_;
};
#endif
#include "../explicitvectors.hh"
#include "../program_state.hh"
using MyProgramState = ProgramState<Vector, ScalarVector>;
template class RestartIO<MyProgramState>;
#ifndef SRC_HDF5_RESTRICT_HH
#define SRC_HDF5_RESTRICT_HH
#include <cassert>
#include <dune/common/bitsetvector.hh>
#include "../tobool.hh"
template <class Vector, class Patch>
Vector restrictToSurface(Vector const &v1, Patch const &patch) {
auto const &vertices = *patch.getVertices();
assert(vertices.size() == v1.size());
Vector ret(vertices.count());
auto target = ret.begin();
for (size_t i = 0; i < v1.size(); ++i)
if (toBool(vertices[i]))
*(target++) = v1[i];
assert(target == ret.end());
return ret;
}
#endif
#ifndef SRC_HDF_SURFACE_WRITER_HH
#define SRC_HDF_SURFACE_WRITER_HH
#include <dune/fufem/boundarypatch.hh>
#include <dune/fufem/hdf5/sequenceio.hh>
#include <dune/fufem/hdf5/singletonwriter.hh>
template <class ProgramState, class GridView> class SurfaceWriter {
using Vector = typename ProgramState::Vector;
using Patch = BoundaryPatch<GridView>;
public:
SurfaceWriter(HDF5::Grouplike &file, Vector const &vertexCoordinates,
Patch const &surface);
void write(ProgramState const &programState);
private:
HDF5::Group group_;
Patch const &surface_;
HDF5::SequenceIO<2> surfaceDisplacementWriter_;
HDF5::SequenceIO<2> surfaceVelocityWriter_;
};
#endif
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "time-writer.hh"
template <class ProgramState>
TimeWriter<ProgramState>::TimeWriter(HDF5::Grouplike &file)
: file_(file),
relativeTimeWriter_(file_, "relativeTime"),
relativeTimeIncrementWriter_(file_, "relativeTimeIncrement") {}
template <class ProgramState>
void TimeWriter<ProgramState>::write(ProgramState const &programState) {
addEntry(relativeTimeWriter_, programState.timeStep,
programState.relativeTime);
addEntry(relativeTimeIncrementWriter_, programState.timeStep,
programState.relativeTau);
}
#include "time-writer_tmpl.cc"
#ifndef SRC_HDF_TIME_WRITER_HH
#define SRC_HDF_TIME_WRITER_HH
#include <dune/fufem/hdf5/file.hh>
#include <dune/fufem/hdf5/sequenceio.hh>
template <class ProgramState> class TimeWriter {
public:
TimeWriter(HDF5::Grouplike &file);
void write(ProgramState const &programState);
private:
HDF5::Grouplike &file_;
HDF5::SequenceIO<0> relativeTimeWriter_;
HDF5::SequenceIO<0> relativeTimeIncrementWriter_;
};
#endif
#include "../explicitvectors.hh"
#include "../program_state.hh"
using MyProgramState = ProgramState<Vector, ScalarVector>;
template class TimeWriter<MyProgramState>;
#ifndef SRC_MATRICES_HH
#define SRC_MATRICES_HH
template <class Matrix> struct Matrices {
Matrix elasticity;
Matrix damping;
Matrix mass;
};
#endif
add_custom_target(tectonic_src_multi-body-problem SOURCES
multi-body-problem.cfg
multi-body-problem-2D.cfg
multi-body-problem-3D.cfg
)
set(MSW_SOURCE_FILES
../../dune/tectonic/assemblers.cc
../../dune/tectonic/data-structures/body/body.cc
../../dune/tectonic/data-structures/network/levelcontactnetwork.cc
../../dune/tectonic/data-structures/network/contactnetwork.cc
../../dune/tectonic/data-structures/enumparser.cc
#../../dune/tectonic/factories/cantorfactory.cc
../../dune/tectonic/factories/threeblocksfactory.cc
../../dune/tectonic/factories/stackedblocksfactory.cc
#../../dune/tectonic/io/vtk.cc
#../../dune/tectonic/io/hdf5/frictionalboundary-writer.cc
#../../dune/tectonic/io/hdf5/iteration-writer.cc
#../../dune/tectonic/io/hdf5/patchinfo-writer.cc
#../../dune/tectonic/io/hdf5/restart-io.cc
#../../dune/tectonic/io/hdf5/surface-writer.cc
#../../dune/tectonic/io/hdf5/time-writer.cc
../../dune/tectonic/problem-data/grid/cuboidgeometry.cc
../../dune/tectonic/problem-data/grid/mygrids.cc
../../dune/tectonic/problem-data/grid/simplexmanager.cc
../../dune/tectonic/spatial-solving/solverfactory.cc
../../dune/tectonic/spatial-solving/fixedpointiterator.cc
../../dune/tectonic/time-stepping/coupledtimestepper.cc
../../dune/tectonic/time-stepping/adaptivetimestepper.cc
../../dune/tectonic/time-stepping/rate.cc
../../dune/tectonic/time-stepping/rate/rateupdater.cc
../../dune/tectonic/time-stepping/state.cc
multi-body-problem.cc
)
foreach(_dim 2 3)
set(_msw_target multi-body-problem-${_dim}D)
add_executable(${_msw_target} ${MSW_SOURCE_FILES})
add_dune_ug_flags(${_msw_target})
add_dune_hdf5_flags(${_msw_target})
set_property(TARGET ${_msw_target} APPEND PROPERTY COMPILE_DEFINITIONS "MY_DIM=${_dim}")
#set_property(TARGET ${_msw_target} APPEND PROPERTY COMPILE_DEFINITIONS "NEW_TNNMG_COMPUTE_ITERATES_DIRECTLY=1")
endforeach()
# -*- mode:conf -*- # -*- mode:conf -*-
[boundary.friction] [boundary.friction]
smallestDiameter= 2e-3 # [m] smallestDiameter = 0.05 # 0.05 2e-3 [m]
[timeSteps] [timeSteps]
refinementTolerance = 1e-5 refinementTolerance = 2e-2 # 1e-5
[u0.solver] [u0.solver]
tolerance = 1e-8 tolerance = 1e-8
...@@ -17,5 +17,8 @@ tolerance = 1e-8 ...@@ -17,5 +17,8 @@ tolerance = 1e-8
[v.fpi] [v.fpi]
tolerance = 1e-5 tolerance = 1e-5
[solver.tnnmg.linear] [solver.tnnmg.preconditioner.basesolver]
tolerance = 1e-10
[solver.tnnmg.preconditioner.patchsolver]
tolerance = 1e-10 tolerance = 1e-10