BDFOdeSolver

Velocity-based ODE solver using Backward Differentiation Formula (BDF), at any order, supporting variable time step size.

Target: Sofa.Component.ODESolver.Backward

namespace: sofa::component::odesolver::backward

parents:

• BaseLinearMultiStepMethod

Data

Name	Description	Default value
name	object name	unnamed
printLog	if true, emits extra messages at runtime.	0
tags	list of the subsets the object belongs to
bbox	this object bounding box
componentState	The state of the component among (Dirty, Valid, Undefined, Loading, Invalid).	Undefined
listening	if true, handle the events, otherwise ignore the events	0
order	Order of the numerical method	1
rayleighStiffness	Rayleigh damping coefficient related to stiffness, > 0	0
rayleighMass	Rayleigh damping coefficient related to mass, > 0	0

Links

Name	Description	Destination type name
context	Graph Node containing this object (or BaseContext::getDefault() if no graph is used)	BaseContext
slaves	Sub-objects used internally by this object	BaseObject
master	nullptr for regular objects, or master object for which this object is one sub-objects	BaseObject
linearSolver	Linear solver used by this component	LinearSolver
newtonSolver	Link to a Newton-Raphson solver to solve the nonlinear equation produced by this numerical method	NewtonRaphsonSolver

Examples

BDFOdeSolver.scn

XMLPython

<Node name="root" gravity="-1.8 0 100" dt="0.01">

    <Node name="plugins">
        <RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [FixedProjectiveConstraint] -->
        <RequiredPlugin name="Sofa.Component.Engine.Select"/> <!-- Needed to use components [BoxROI] -->
        <RequiredPlugin name="Sofa.Component.IO.Mesh"/> <!-- Needed to use components [MeshGmshLoader,MeshOBJLoader] -->
        <RequiredPlugin name="Sofa.Component.LinearSolver.Direct"/> <!-- Needed to use components [EigenSimplicialLDLT] -->
        <RequiredPlugin name="Sofa.Component.LinearSystem"/> <!-- Needed to use components [ConstantSparsityPatternSystem] -->
        <RequiredPlugin name="Sofa.Component.Mapping.Linear"/> <!-- Needed to use components [BarycentricMapping] -->
        <RequiredPlugin name="Sofa.Component.Mass"/> <!-- Needed to use components [MeshMatrixMass] -->
        <RequiredPlugin name="Sofa.Component.ODESolver.Backward"/> <!-- Needed to use components [BDFOdeSolver,NewtonRaphsonSolver] -->
        <RequiredPlugin name="Sofa.Component.SolidMechanics.FEM.HyperElastic"/> <!-- Needed to use components [TetrahedronHyperelasticityFEMForceField] -->
        <RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
        <RequiredPlugin name="Sofa.Component.Topology.Container.Dynamic"/> <!-- Needed to use components [TetrahedronSetGeometryAlgorithms,TetrahedronSetTopologyContainer] -->
        <RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [VisualStyle] -->
        <RequiredPlugin name="Sofa.GL.Component.Rendering3D"/> <!-- Needed to use components [OglModel] -->
    </Node>

    <VisualStyle displayFlags="showWireframe showVisual showBehaviorModels hideForceFields" />
    <DefaultAnimationLoop parallelODESolving="false"/>

    <Node name="DeformableObject">

        <BDFOdeSolver order="2" printLog="false" rayleighMass="0.01" rayleighStiffness="0.01"/>
        <NewtonRaphsonSolver name="newton" printLog="false"
                             maxNbIterationsNewton="10" absoluteResidualStoppingThreshold="1e-5"
                             maxNbIterationsLineSearch="5" lineSearchCoefficient="0.5"
                             relativeInitialStoppingThreshold="1e-3"
                             absoluteEstimateDifferenceThreshold="1e-5"
                             relativeEstimateDifferenceThreshold="1e-5"/>
        <ConstantSparsityPatternSystem template="CompressedRowSparseMatrix" name="A" checkIndices="false"/>
        <PCGLinearSolver name="PCG" iterations="1000" preconditioner="@preconditioner"/>
        <AsyncSparseLDLSolver name="preconditioner"/>

        <MeshGmshLoader name="loader" filename="mesh/truthcylinder1.msh" />
        <TetrahedronSetTopologyContainer src="@loader" name="topologyContainer"/>
        <TetrahedronSetGeometryAlgorithms name="geomAlgo"/>
        <MechanicalObject src="@loader" />
        <MeshMatrixMass totalMass="15" topology="@topologyContainer"/>

        <BoxROI name="box" box="-10 -20 -10  10 -17.5 10" drawBoxes="true"/>
        <FixedProjectiveConstraint indices="@box.indices" />
        <TetrahedronHyperelasticityFEMForceField name="FEM" ParameterSet="3448.2759 31034.483" materialName="StVenantKirchhoff"/>

        <Node name="visual">
            <MeshOBJLoader name="meshLoader_0" filename="mesh/truthcylinder1.obj" handleSeams="1" />
            <OglModel name="Visual" src="@meshLoader_0" color="red" />
            <BarycentricMapping input="@.." output="@Visual" />
        </Node>
    </Node>

</Node>

def createScene(root_node):

   root = root_node.addChild('root', gravity="-1.8 0 100", dt="0.01")

   plugins = root.addChild('plugins')

   plugins.addObject('RequiredPlugin', name="Sofa.Component.Constraint.Projective")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Engine.Select")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.IO.Mesh")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Direct")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.LinearSystem")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Mapping.Linear")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Mass")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.ODESolver.Backward")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.SolidMechanics.FEM.HyperElastic")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.StateContainer")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Topology.Container.Dynamic")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Visual")
   plugins.addObject('RequiredPlugin', name="Sofa.GL.Component.Rendering3D")

   root.addObject('VisualStyle', displayFlags="showWireframe showVisual showBehaviorModels hideForceFields")
   root.addObject('DefaultAnimationLoop', parallelODESolving="false")

   deformable_object = root.addChild('DeformableObject')

   deformable_object.addObject('BDFOdeSolver', order="2", printLog="false", rayleighMass="0.01", rayleighStiffness="0.01")
   deformable_object.addObject('NewtonRaphsonSolver', name="newton", printLog="false", maxNbIterationsNewton="10", absoluteResidualStoppingThreshold="1e-5", maxNbIterationsLineSearch="5", lineSearchCoefficient="0.5", relativeInitialStoppingThreshold="1e-3", absoluteEstimateDifferenceThreshold="1e-5", relativeEstimateDifferenceThreshold="1e-5")
   deformable_object.addObject('ConstantSparsityPatternSystem', template="CompressedRowSparseMatrix", name="A", checkIndices="false")
   deformable_object.addObject('PCGLinearSolver', name="PCG", iterations="1000", preconditioner="@preconditioner")
   deformable_object.addObject('AsyncSparseLDLSolver', name="preconditioner")
   deformable_object.addObject('MeshGmshLoader', name="loader", filename="mesh/truthcylinder1.msh")
   deformable_object.addObject('TetrahedronSetTopologyContainer', src="@loader", name="topologyContainer")
   deformable_object.addObject('TetrahedronSetGeometryAlgorithms', name="geomAlgo")
   deformable_object.addObject('MechanicalObject', src="@loader")
   deformable_object.addObject('MeshMatrixMass', totalMass="15", topology="@topologyContainer")
   deformable_object.addObject('BoxROI', name="box", box="-10 -20 -10  10 -17.5 10", drawBoxes="true")
   deformable_object.addObject('FixedProjectiveConstraint', indices="@box.indices")
   deformable_object.addObject('TetrahedronHyperelasticityFEMForceField', name="FEM", ParameterSet="3448.2759 31034.483", materialName="StVenantKirchhoff")

   visual = DeformableObject.addChild('visual')

   visual.addObject('MeshOBJLoader', name="meshLoader_0", filename="mesh/truthcylinder1.obj", handleSeams="1")
   visual.addObject('OglModel', name="Visual", src="@meshLoader_0", color="red")
   visual.addObject('BarycentricMapping', input="@..", output="@Visual")

BDFOdeSolver_spring1d.scn

XMLPython

<Node name="root" gravity="-9.81 0 0" dt="0.01">
    <RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [FixedProjectiveConstraint] -->
    <RequiredPlugin name="Sofa.Component.LinearSolver.Direct"/> <!-- Needed to use components [EigenSimplicialLDLT] -->
    <RequiredPlugin name="Sofa.Component.Mass"/> <!-- Needed to use components [MeshMatrixMass] -->
    <RequiredPlugin name="Sofa.Component.ODESolver.Backward"/> <!-- Needed to use components [NewtonRaphsonSolver] -->
    <RequiredPlugin name="Sofa.Component.ODESolver.Integration"/> <!-- Needed to use components [BDF1] -->
    <RequiredPlugin name="Sofa.Component.SolidMechanics.Spring"/> <!-- Needed to use components [SpringForceField] -->
    <RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
    <RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [VisualStyle] -->
    <RequiredPlugin name="Sofa.GL.Component.Rendering3D"/> <!-- Needed to use components [OglCylinderModel] -->
    <RequiredPlugin name="Sofa.Component.Topology.Container.Dynamic"/> <!-- Needed to use components [EdgeSetTopologyContainer] -->

    <VisualStyle displayFlags="showWireframe showVisual showBehaviorModels showForceFields" />
    <DefaultAnimationLoop/>
    <VisualGrid size="2"/>
    <LineAxis size="2"/>

    <Node name="BDF-1">

        <BDFOdeSolver order="1" printLog="false" rayleighMass="0.01" rayleighStiffness="0.01"/>
        <NewtonRaphsonSolver name="newton" printLog="false" maxNbIterationsNewton="4" maxNbIterationsLineSearch="2" absoluteResidualStoppingThreshold="1e-6"/>
        <EigenSimplicialLDLT template="CompressedRowSparseMatrix"/>

        <MechanicalObject name="dofs" template="Vec1" position="1 " rest_position="0" showObject="true" showObjectScale="20"/>
        <PointSetTopologyContainer name="topologyContainer" position="1"/>
        <UniformMass totalMass="1" topology="@topologyContainer"/>
        <RestShapeSpringsForceField points="0"/>
    </Node>

    <Node name="BDF-2">

        <BDFOdeSolver order="2" printLog="false" rayleighMass="0.01" rayleighStiffness="0.01"/>
        <NewtonRaphsonSolver name="newton" printLog="false" maxNbIterationsNewton="4" maxNbIterationsLineSearch="2" absoluteResidualStoppingThreshold="1e-6"/>
        <EigenSimplicialLDLT template="CompressedRowSparseMatrix"/>

        <MechanicalObject name="dofs" template="Vec1" position="1 " rest_position="0" showObject="true" showObjectScale="20"/>
        <PointSetTopologyContainer name="topologyContainer" position="1"/>
        <UniformMass totalMass="1" topology="@topologyContainer"/>
        <RestShapeSpringsForceField points="0"/>
    </Node>

    <Node name="BDF-3">

        <BDFOdeSolver order="3" printLog="false" rayleighMass="0.01" rayleighStiffness="0.01"/>
        <NewtonRaphsonSolver name="newton" printLog="false" maxNbIterationsNewton="4" maxNbIterationsLineSearch="2" absoluteResidualStoppingThreshold="1e-6"/>
        <EigenSimplicialLDLT template="CompressedRowSparseMatrix"/>

        <MechanicalObject name="dofs" template="Vec1" position="1 " rest_position="0" showObject="true" showObjectScale="20"/>
        <PointSetTopologyContainer name="topologyContainer" position="1"/>
        <UniformMass totalMass="1" topology="@topologyContainer"/>
        <RestShapeSpringsForceField points="0"/>
    </Node>

</Node>

def createScene(root_node):

   root = root_node.addChild('root', gravity="-9.81 0 0", dt="0.01")

   root.addObject('RequiredPlugin', name="Sofa.Component.Constraint.Projective")
   root.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Direct")
   root.addObject('RequiredPlugin', name="Sofa.Component.Mass")
   root.addObject('RequiredPlugin', name="Sofa.Component.ODESolver.Backward")
   root.addObject('RequiredPlugin', name="Sofa.Component.ODESolver.Integration")
   root.addObject('RequiredPlugin', name="Sofa.Component.SolidMechanics.Spring")
   root.addObject('RequiredPlugin', name="Sofa.Component.StateContainer")
   root.addObject('RequiredPlugin', name="Sofa.Component.Visual")
   root.addObject('RequiredPlugin', name="Sofa.GL.Component.Rendering3D")
   root.addObject('RequiredPlugin', name="Sofa.Component.Topology.Container.Dynamic")
   root.addObject('VisualStyle', displayFlags="showWireframe showVisual showBehaviorModels showForceFields")
   root.addObject('DefaultAnimationLoop', )
   root.addObject('VisualGrid', size="2")
   root.addObject('LineAxis', size="2")

   bdf_1 = root.addChild('BDF-1')

   bdf_1.addObject('BDFOdeSolver', order="1", printLog="false", rayleighMass="0.01", rayleighStiffness="0.01")
   bdf_1.addObject('NewtonRaphsonSolver', name="newton", printLog="false", maxNbIterationsNewton="4", maxNbIterationsLineSearch="2", absoluteResidualStoppingThreshold="1e-6")
   bdf_1.addObject('EigenSimplicialLDLT', template="CompressedRowSparseMatrix")
   bdf_1.addObject('MechanicalObject', name="dofs", template="Vec1", position="1 ", rest_position="0", showObject="true", showObjectScale="20")
   bdf_1.addObject('PointSetTopologyContainer', name="topologyContainer", position="1")
   bdf_1.addObject('UniformMass', totalMass="1", topology="@topologyContainer")
   bdf_1.addObject('RestShapeSpringsForceField', points="0")

   bdf_2 = root.addChild('BDF-2')

   bdf_2.addObject('BDFOdeSolver', order="2", printLog="false", rayleighMass="0.01", rayleighStiffness="0.01")
   bdf_2.addObject('NewtonRaphsonSolver', name="newton", printLog="false", maxNbIterationsNewton="4", maxNbIterationsLineSearch="2", absoluteResidualStoppingThreshold="1e-6")
   bdf_2.addObject('EigenSimplicialLDLT', template="CompressedRowSparseMatrix")
   bdf_2.addObject('MechanicalObject', name="dofs", template="Vec1", position="1 ", rest_position="0", showObject="true", showObjectScale="20")
   bdf_2.addObject('PointSetTopologyContainer', name="topologyContainer", position="1")
   bdf_2.addObject('UniformMass', totalMass="1", topology="@topologyContainer")
   bdf_2.addObject('RestShapeSpringsForceField', points="0")

   bdf_3 = root.addChild('BDF-3')

   bdf_3.addObject('BDFOdeSolver', order="3", printLog="false", rayleighMass="0.01", rayleighStiffness="0.01")
   bdf_3.addObject('NewtonRaphsonSolver', name="newton", printLog="false", maxNbIterationsNewton="4", maxNbIterationsLineSearch="2", absoluteResidualStoppingThreshold="1e-6")
   bdf_3.addObject('EigenSimplicialLDLT', template="CompressedRowSparseMatrix")
   bdf_3.addObject('MechanicalObject', name="dofs", template="Vec1", position="1 ", rest_position="0", showObject="true", showObjectScale="20")
   bdf_3.addObject('PointSetTopologyContainer', name="topologyContainer", position="1")
   bdf_3.addObject('UniformMass', totalMass="1", topology="@topologyContainer")
   bdf_3.addObject('RestShapeSpringsForceField', points="0")

BDFOdeSolver_spring3d.scn

XMLPython

<Node name="root" gravity="0 -9.81 0" dt="0.01">

    <Node name="plugins">
        <RequiredPlugin name="Sofa.Component.Constraint.Projective"/> <!-- Needed to use components [FixedProjectiveConstraint] -->
        <RequiredPlugin name="Sofa.Component.LinearSolver.Direct"/> <!-- Needed to use components [EigenSimplicialLDLT] -->
        <RequiredPlugin name="Sofa.Component.Mass"/> <!-- Needed to use components [UniformMass] -->
        <RequiredPlugin name="Sofa.Component.ODESolver.Backward"/> <!-- Needed to use components [BDFOdeSolver,NewtonRaphsonSolver] -->
        <RequiredPlugin name="Sofa.Component.SolidMechanics.Spring"/> <!-- Needed to use components [SpringForceField] -->
        <RequiredPlugin name="Sofa.Component.StateContainer"/> <!-- Needed to use components [MechanicalObject] -->
        <RequiredPlugin name="Sofa.Component.Topology.Container.Dynamic"/> <!-- Needed to use components [EdgeSetTopologyContainer] -->
        <RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [LineAxis,VisualGrid,VisualStyle] -->
    </Node>

    <VisualStyle displayFlags="showWireframe showVisual showBehaviorModels showForceFields" />
    <DefaultAnimationLoop/>
    <VisualGrid size="2"/>
    <LineAxis size="2"/>

    <Node name="BDF-1">

        <BDFOdeSolver order="1" printLog="false" rayleighMass="0.01" rayleighStiffness="0.01"/>
        <NewtonRaphsonSolver name="newton" printLog="false" maxNbIterationsNewton="4" maxNbIterationsLineSearch="2" absoluteResidualStoppingThreshold="1e-6"/>
        <EigenSimplicialLDLT template="CompressedRowSparseMatrix"/>

        <MechanicalObject name="dofs" template="Vec3" position="0 0 0  1 1 0 " showObject="true" showObjectScale="20"/>
        <EdgeSetTopologyContainer name="topologyContainer" edges="0 1" position="@dofs.position"/>
        <UniformMass totalMass="15" topology="@topologyContainer"/>
        <SpringForceField spring="0 1 1000 0 1"/>
        <FixedProjectiveConstraint indices="0" />

    </Node>

    <Node name="BDF-2">

        <BDFOdeSolver order="2" printLog="false" rayleighMass="0.01" rayleighStiffness="0.01"/>
        <NewtonRaphsonSolver name="newton" printLog="false" maxNbIterationsNewton="4" maxNbIterationsLineSearch="2" absoluteResidualStoppingThreshold="1e-6"/>
        <EigenSimplicialLDLT template="CompressedRowSparseMatrix"/>

        <MechanicalObject name="dofs" template="Vec3" position="0 0 0  1 1 0 " showObject="true" showObjectScale="20"/>
        <EdgeSetTopologyContainer name="topologyContainer" edges="0 1" position="@dofs.position"/>
        <UniformMass totalMass="15" topology="@topologyContainer"/>
        <SpringForceField spring="0 1 1000 0 1"/>
        <FixedProjectiveConstraint indices="0" />

    </Node>

    <Node name="BDF-3">

        <BDFOdeSolver order="3" printLog="false" rayleighMass="0.01" rayleighStiffness="0.01"/>
        <NewtonRaphsonSolver name="newton" printLog="false" maxNbIterationsNewton="4" maxNbIterationsLineSearch="2" absoluteResidualStoppingThreshold="1e-6"/>
        <EigenSimplicialLDLT template="CompressedRowSparseMatrix"/>

        <MechanicalObject name="dofs" template="Vec3" position="0 0 0  1 1 0 " showObject="true" showObjectScale="20"/>
        <EdgeSetTopologyContainer name="topologyContainer" edges="0 1" position="@dofs.position"/>
        <UniformMass totalMass="15" topology="@topologyContainer"/>
        <SpringForceField spring="0 1 1000 0 1"/>
        <FixedProjectiveConstraint indices="0" />

    </Node>
</Node>

def createScene(root_node):

   root = root_node.addChild('root', gravity="0 -9.81 0", dt="0.01")

   plugins = root.addChild('plugins')

   plugins.addObject('RequiredPlugin', name="Sofa.Component.Constraint.Projective")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.LinearSolver.Direct")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Mass")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.ODESolver.Backward")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.SolidMechanics.Spring")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.StateContainer")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Topology.Container.Dynamic")
   plugins.addObject('RequiredPlugin', name="Sofa.Component.Visual")

   root.addObject('VisualStyle', displayFlags="showWireframe showVisual showBehaviorModels showForceFields")
   root.addObject('DefaultAnimationLoop', )
   root.addObject('VisualGrid', size="2")
   root.addObject('LineAxis', size="2")

   bdf_1 = root.addChild('BDF-1')

   bdf_1.addObject('BDFOdeSolver', order="1", printLog="false", rayleighMass="0.01", rayleighStiffness="0.01")
   bdf_1.addObject('NewtonRaphsonSolver', name="newton", printLog="false", maxNbIterationsNewton="4", maxNbIterationsLineSearch="2", absoluteResidualStoppingThreshold="1e-6")
   bdf_1.addObject('EigenSimplicialLDLT', template="CompressedRowSparseMatrix")
   bdf_1.addObject('MechanicalObject', name="dofs", template="Vec3", position="0 0 0  1 1 0 ", showObject="true", showObjectScale="20")
   bdf_1.addObject('EdgeSetTopologyContainer', name="topologyContainer", edges="0 1", position="@dofs.position")
   bdf_1.addObject('UniformMass', totalMass="15", topology="@topologyContainer")
   bdf_1.addObject('SpringForceField', spring="0 1 1000 0 1")
   bdf_1.addObject('FixedProjectiveConstraint', indices="0")

   bdf_2 = root.addChild('BDF-2')

   bdf_2.addObject('BDFOdeSolver', order="2", printLog="false", rayleighMass="0.01", rayleighStiffness="0.01")
   bdf_2.addObject('NewtonRaphsonSolver', name="newton", printLog="false", maxNbIterationsNewton="4", maxNbIterationsLineSearch="2", absoluteResidualStoppingThreshold="1e-6")
   bdf_2.addObject('EigenSimplicialLDLT', template="CompressedRowSparseMatrix")
   bdf_2.addObject('MechanicalObject', name="dofs", template="Vec3", position="0 0 0  1 1 0 ", showObject="true", showObjectScale="20")
   bdf_2.addObject('EdgeSetTopologyContainer', name="topologyContainer", edges="0 1", position="@dofs.position")
   bdf_2.addObject('UniformMass', totalMass="15", topology="@topologyContainer")
   bdf_2.addObject('SpringForceField', spring="0 1 1000 0 1")
   bdf_2.addObject('FixedProjectiveConstraint', indices="0")

   bdf_3 = root.addChild('BDF-3')

   bdf_3.addObject('BDFOdeSolver', order="3", printLog="false", rayleighMass="0.01", rayleighStiffness="0.01")
   bdf_3.addObject('NewtonRaphsonSolver', name="newton", printLog="false", maxNbIterationsNewton="4", maxNbIterationsLineSearch="2", absoluteResidualStoppingThreshold="1e-6")
   bdf_3.addObject('EigenSimplicialLDLT', template="CompressedRowSparseMatrix")
   bdf_3.addObject('MechanicalObject', name="dofs", template="Vec3", position="0 0 0  1 1 0 ", showObject="true", showObjectScale="20")
   bdf_3.addObject('EdgeSetTopologyContainer', name="topologyContainer", edges="0 1", position="@dofs.position")
   bdf_3.addObject('UniformMass', totalMass="15", topology="@topologyContainer")
   bdf_3.addObject('SpringForceField', spring="0 1 1000 0 1")
   bdf_3.addObject('FixedProjectiveConstraint', indices="0")