diff --git a/Sofa/Component/Constraint/Lagrangian/Solver/src/sofa/component/constraint/lagrangian/solver/LCPConstraintSolver.cpp b/Sofa/Component/Constraint/Lagrangian/Solver/src/sofa/component/constraint/lagrangian/solver/LCPConstraintSolver.cpp
index 22f7f043714..f2317f710a7 100644
--- a/Sofa/Component/Constraint/Lagrangian/Solver/src/sofa/component/constraint/lagrangian/solver/LCPConstraintSolver.cpp
+++ b/Sofa/Component/Constraint/Lagrangian/Solver/src/sofa/component/constraint/lagrangian/solver/LCPConstraintSolver.cpp
@@ -99,6 +99,7 @@ bool LCPConstraintSolver::prepareStates(const core::ConstraintParams * /*cParams
     msg_info() <<" propagate DXn performed - collision called" ;
 
     SCOPED_TIMER("resetContactForce");
+  
     for (const auto& cc : l_constraintCorrections)
     {
         cc->resetContactForce();
@@ -1026,7 +1027,7 @@ int LCPConstraintSolver::lcp_gaussseidel_unbuilt(SReal *dfree, SReal *f, std::ve
     {
         bool elem1 = false;
         bool elem2 = false;
-        for (const auto cc : l_constraintCorrections)
+        for (const auto& cc : l_constraintCorrections)
         {
             if(cc->hasConstraintNumber(c1))
             {
diff --git a/Sofa/Component/LinearSystem/src/sofa/component/linearsystem/ConstantSparsityPatternSystem.inl b/Sofa/Component/LinearSystem/src/sofa/component/linearsystem/ConstantSparsityPatternSystem.inl
index 565e95689b8..7409254c279 100644
--- a/Sofa/Component/LinearSystem/src/sofa/component/linearsystem/ConstantSparsityPatternSystem.inl
+++ b/Sofa/Component/LinearSystem/src/sofa/component/linearsystem/ConstantSparsityPatternSystem.inl
@@ -263,7 +263,8 @@ void ConstantSparsityPatternSystem<TMatrix, TVector>::resizeSystem(sofa::Size n)
 
     if (this->getSystemMatrix())
     {
-        if (n != this->getSystemMatrix()->rowSize() || n != this->getSystemMatrix()->colSize())
+        Index nIndex = sofa::helper::narrow_cast<Index>(n);
+        if (nIndex != this->getSystemMatrix()->rowSize() || nIndex != this->getSystemMatrix()->colSize())
         {
             this->getSystemMatrix()->resize(n, n);
         }
@@ -336,12 +337,6 @@ void ConstantSparsityPatternSystem<TMatrix, TVector>::preAssembleSystem(const co
 
     if (isConstantSparsityPatternUsedYet())
     {
-        // this->getSystemMatrix()->compressed = true;
-        for (const auto& mat : this->m_localMappedMatrices)
-        {
-            // mat.second->compressed = true;
-        }
-
         reinitLocalMatrices(this->template getLocalMatrixMap<Contribution::STIFFNESS>());
         reinitLocalMatrices(this->template getLocalMatrixMap<Contribution::MASS>());
         reinitLocalMatrices(this->template getLocalMatrixMap<Contribution::DAMPING>());
diff --git a/Sofa/Component/MechanicalLoad/src/sofa/component/mechanicalload/EllipsoidForceField.inl b/Sofa/Component/MechanicalLoad/src/sofa/component/mechanicalload/EllipsoidForceField.inl
index c93af64a589..4459517d8eb 100644
--- a/Sofa/Component/MechanicalLoad/src/sofa/component/mechanicalload/EllipsoidForceField.inl
+++ b/Sofa/Component/MechanicalLoad/src/sofa/component/mechanicalload/EllipsoidForceField.inl
@@ -104,11 +104,14 @@ void EllipsoidForceField<DataTypes>::addForce(const sofa::core::MechanicalParams
     const Real stiffabs = helper::rabs(stiffness);
     //const Real s2 = (stiff < 0 ? - stiff*stiff : stiff*stiff );
     Coord inv_r2;
-    for (int j=0; j<N; j++) inv_r2[j] = 1/(r[j]*r[j]);
+    for (unsigned int j=0; j<N; j++)
+    {
+        inv_r2[j] = 1 / (r[j] * r[j]);
+    }
     sofa::type::vector<Contact>* contacts = this->d_contacts.beginEdit();
     contacts->clear();
     f1.resize(p1.size());
-    for (unsigned int i=0; i<p1.size(); i++)
+    for (Size i=0; i<p1.size(); i++)
     {
         Coord dp = p1[i] - center;
         Real norm2 = 0;
@@ -119,7 +122,10 @@ void EllipsoidForceField<DataTypes>::addForce(const sofa::core::MechanicalParams
             Real norm = helper::rsqrt(norm2);
             Real v = norm-1;
             Coord grad;
-            for (int j=0; j<N; j++) grad[j] = dp[j]*inv_r2[j];
+            for (unsigned int j=0; j<N; j++)
+            {
+                grad[j] = dp[j]*inv_r2[j];
+            }
             Real gnorm2 = grad.norm2();
             Real gnorm = helper::rsqrt(gnorm2);
             //grad /= gnorm; //.normalize();
@@ -132,9 +138,9 @@ void EllipsoidForceField<DataTypes>::addForce(const sofa::core::MechanicalParams
             Real fact1 = -stiffabs / (norm * gnorm);
             Real fact2 = -stiffabs*v / gnorm;
             Real fact3 = -stiffabs*v / gnorm2;
-            for (int ci = 0; ci < N; ++ci)
+            for (unsigned int ci = 0; ci < N; ++ci)
             {
-                for (int cj = 0; cj < N; ++cj)
+                for (unsigned int cj = 0; cj < N; ++cj)
                     c.m[ci][cj] = grad[ci]*grad[cj] * (fact1 + fact3*inv_r2[cj]);
                 c.m[ci][ci] += fact2*inv_r2[ci];
             }
diff --git a/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixConstraintEigenUtils.h b/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixConstraintEigenUtils.h
index 8627f175666..dfdb2afd0c8 100644
--- a/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixConstraintEigenUtils.h
+++ b/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixConstraintEigenUtils.h
@@ -203,7 +203,7 @@ void addMultTransposeEigen(LhsMatrixDeriv& lhs, const Eigen::SparseMatrix<Real,
                     // check the next LhsDeriv::total_size rows for potential non zero values
                     // inside the block [k, bCol, k+LhsDeriv::total_size, bCol+RhsDeriv::total_size]
                     bool blockEmpty = true;
-                    for (int j = 0; j < LhsDeriv::total_size; ++j)
+                    for (Size j = 0; j < LhsDeriv::total_size; ++j)
                     {
                         typename EigenSparseMatrix::InnerIterator it(jacobianT, k+j);
                         // advance until we are either invalid or inside the block
diff --git a/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixGeneric.h b/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixGeneric.h
index 9b1ee95f6a5..26216ac517b 100644
--- a/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixGeneric.h
+++ b/Sofa/framework/LinearAlgebra/src/sofa/linearalgebra/CompressedRowSparseMatrixGeneric.h
@@ -1433,7 +1433,7 @@ public :
 
         if( m.rowIndex.empty() ) return; // if m is null
 
-        for( Index xi = 0 ; xi < rowIndex.size() ; ++xi )  // for each non-null transpose block column
+        for( Size xi = 0 ; xi < rowIndex.size() ; ++xi )  // for each non-null transpose block column
         {
             unsigned mr = 0; // block row index in m
 
diff --git a/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.cpp b/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.cpp
index 9295c9ac93c..fddae4663b4 100644
--- a/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.cpp
+++ b/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.cpp
@@ -296,9 +296,9 @@ using sofa::helper::logging::MessageDispatcher;
 using sofa::helper::logging::LoggingMessageHandler;
 
 SofaPhysicsSimulation::SofaPhysicsSimulation(bool useGUI_, int GUIFramerate_)
-    : useGUI(useGUI_)
+    : m_msgIsActivated(false)
+    , useGUI(useGUI_)
     , GUIFramerate(GUIFramerate_)
-    , m_msgIsActivated(false)
 {
     sofa::helper::init();
     static bool first = true;
@@ -339,8 +339,7 @@ SofaPhysicsSimulation::SofaPhysicsSimulation(bool useGUI_, int GUIFramerate_)
     lastH = 0;
     vparams = sofa::core::visual::VisualParams::defaultInstance();
 
-    m_Simulation = new sofa::simulation::graph::DAGSimulation();
-    sofa::simulation::setSimulation(m_Simulation);
+    assert(sofa::simulation::getSimulation());
 
     sofa::component::init(); // force dependency on Sofa.Component
 
@@ -396,12 +395,12 @@ int SofaPhysicsSimulation::load(const char* cfilename)
     sofa::helper::BackTrace::autodump();
 
     sofa::helper::system::DataRepository.findFile(filename);
-    m_RootNode = m_Simulation->load(filename.c_str());
+    m_RootNode = sofa::simulation::node::load(filename.c_str());
     int result = API_SUCCESS;
     if (m_RootNode.get())
     {
         sceneFileName = filename;
-        m_Simulation->init(m_RootNode.get());
+        sofa::simulation::node::initRoot(m_RootNode.get());
         result = updateOutputMeshes();
 
         if ( useGUI ) {
@@ -410,7 +409,7 @@ int SofaPhysicsSimulation::load(const char* cfilename)
     }
     else
     {
-        m_RootNode = m_Simulation->createNewGraph("");
+        m_RootNode = sofa::simulation::getSimulation()->createNewGraph("");
         return API_SCENE_FAILED;
     }
     initTexturesDone = false;
@@ -425,7 +424,7 @@ int SofaPhysicsSimulation::unload()
 {
     if (m_RootNode.get())
     {
-        m_Simulation->unload(m_RootNode);
+        sofa::simulation::node::unload(m_RootNode);
     }
     else
     {
@@ -471,7 +470,7 @@ void SofaPhysicsSimulation::createScene()
         m_RootNode->setGravity({ 0,-9.8,0 });
         this->createScene_impl();
 
-        m_Simulation->init(m_RootNode.get());
+        sofa::simulation::node::initRoot(m_RootNode.get());
 
         updateOutputMeshes();
     }
@@ -604,7 +603,7 @@ void SofaPhysicsSimulation::reset()
 {
     if (getScene())
     {
-        getSimulation()->reset(getScene());
+        sofa::simulation::node::reset(getScene());
         this->update();
     }
 }
@@ -632,8 +631,8 @@ void SofaPhysicsSimulation::step()
     sofa::simulation::Node* groot = getScene();
     if (!groot) return;
     beginStep();
-    getSimulation()->animate(groot);
-    getSimulation()->updateVisual(groot);
+    sofa::simulation::node::animate(groot);
+    sofa::simulation::node::updateVisual(groot);
     if ( useGUI ) {
       sofa::gui::common::BaseGUI* gui = sofa::gui::common::GUIManager::getGUI();
       gui->stepMainLoop();
@@ -779,7 +778,7 @@ std::string SofaPhysicsSimulation::getMessage(int messageId, int& msgType)
 {
     const std::vector<sofa::helper::logging::Message>& msgs = m_msgHandler->getMessages();
 
-    if (messageId >= msgs.size()) {
+    if (messageId >= (int)msgs.size()) {
         msgType = -1;
         return "Error messageId out of bounds";
     }
@@ -958,7 +957,7 @@ void SofaPhysicsSimulation::drawGL()
         if (!initTexturesDone)
         {
             std::cout << "INIT VISUAL" << std::endl;
-            getSimulation()->initTextures(groot);
+            sofa::simulation::node::initTextures(groot);
             bool setView = false;
             groot->get(currentCamera);
             if (!currentCamera)
@@ -1049,7 +1048,7 @@ void SofaPhysicsSimulation::drawGL()
         glMatrixMode(GL_MODELVIEW);
         glLoadMatrixd(lastModelviewMatrix);
 
-        getSimulation()->draw(vparams,groot);
+        sofa::simulation::node::draw(vparams,groot);
 
         glDisable(GL_LIGHTING);
         glDisable(GL_DEPTH_TEST);
diff --git a/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.h b/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.h
index 05446f685bc..2f1418c702c 100644
--- a/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.h
+++ b/applications/projects/SofaPhysicsAPI/src/SofaPhysicsAPI/SofaPhysicsSimulation.h
@@ -115,7 +115,6 @@ class SOFA_SOFAPHYSICSAPI_API SofaPhysicsSimulation
 #endif
 protected:
 
-    sofa::simulation::Simulation* m_Simulation;
     sofa::simulation::Node::SPtr m_RootNode;
     std::string sceneFileName;
     /// Pointer to the LoggingMessageHandler
@@ -174,7 +173,7 @@ class SOFA_SOFAPHYSICSAPI_API SofaPhysicsSimulation
     }
     sofa::simulation::Simulation* getSimulation() const
     {
-        return m_Simulation;
+        return sofa::simulation::getSimulation();
     }
     sofa::simulation::Node* getScene() const
     {
diff --git a/examples/Demos/caduceus.scn b/examples/Demos/caduceus.scn
index 81eb50261f5..9843110f503 100644
--- a/examples/Demos/caduceus.scn
+++ b/examples/Demos/caduceus.scn
@@ -21,6 +21,7 @@
         <RequiredPlugin name="Sofa.Component.Visual"/> <!-- Needed to use components [InteractiveCamera VisualStyle] -->
         <RequiredPlugin name="Sofa.GL.Component.Rendering3D"/> <!-- Needed to use components [OglModel] -->
         <RequiredPlugin name="Sofa.GL.Component.Shader"/> <!-- Needed to use components [LightManager SpotLight] -->
+        <RequiredPlugin name="Sofa.Component.LinearSystem"/> <!-- Needed to use components [MatrixLinearSystem] -->
     </Node>
     
     <VisualStyle displayFlags="showVisual  " /> <!--showBehaviorModels showCollisionModels-->