diff --git a/Sofa/Component/Mapping/NonLinear/CMakeLists.txt b/Sofa/Component/Mapping/NonLinear/CMakeLists.txt
index 03545b647ce..d97638d9c41 100644
--- a/Sofa/Component/Mapping/NonLinear/CMakeLists.txt
+++ b/Sofa/Component/Mapping/NonLinear/CMakeLists.txt
@@ -8,8 +8,8 @@ set(HEADER_FILES
     ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/init.h
     ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/AreaMapping.h
     ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/AreaMapping.inl
-    ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/AssembledNonLinearMapping.h
-    ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/AssembledNonLinearMapping.inl
+    ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/BaseNonLinearMapping.h
+    ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/BaseNonLinearMapping.inl
     ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/DistanceFromTargetMapping.h
     ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/DistanceFromTargetMapping.inl
     ${SOFACOMPONENTMAPPINGNONLINEAR_SOURCE_DIR}/DistanceMapping.h
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.h b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.h
index 5ee64ed8d88..2392f310364 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.h
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.h
@@ -22,7 +22,7 @@
 #pragma once
 
 #include <sofa/component/mapping/nonlinear/config.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.h>
 #include <sofa/component/mapping/nonlinear/NonLinearMappingData.h>
 #include <sofa/core/topology/BaseMeshTopology.h>
 #include <sofa/linearalgebra/EigenSparseMatrix.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.inl b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.inl
index 1d85b69b91d..0a343e2fc2e 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.inl
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AreaMapping.inl
@@ -21,7 +21,7 @@
 ******************************************************************************/
 #pragma once
 #include <sofa/component/mapping/nonlinear/AreaMapping.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl>
 #include <sofa/core/BaseLocalMappingMatrix.h>
 
 namespace sofa::component::mapping::nonlinear
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/BaseNonLinearMapping.h
similarity index 100%
rename from Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h
rename to Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/BaseNonLinearMapping.h
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl
similarity index 98%
rename from Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl
rename to Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl
index c6cc5ba0c9e..fec4f24a235 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl
@@ -21,7 +21,7 @@
 ******************************************************************************/
 #pragma once
 
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.h>
 #include <sofa/linearalgebra/CompressedRowSparseMatrixConstraintEigenUtils.h>
 
 namespace sofa::component::mapping::nonlinear
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.h b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.h
index 8d7d3c01676..9c226f13918 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.h
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.h
@@ -22,7 +22,7 @@
 #pragma once
 
 #include <sofa/component/mapping/nonlinear/config.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.h>
 #include <sofa/component/mapping/nonlinear/NonLinearMappingData.h>
 #include <sofa/linearalgebra/EigenSparseMatrix.h>
 #include <sofa/type/Mat.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.inl b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.inl
index 31cf683e576..a5fb0255dc6 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.inl
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceFromTargetMapping.inl
@@ -22,7 +22,7 @@
 #pragma once
 
 #include <sofa/component/mapping/nonlinear/DistanceFromTargetMapping.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl>
 #include <sofa/core/BaseLocalMappingMatrix.h>
 #include <sofa/core/behavior/MechanicalState.h>
 #include <sofa/core/visual/VisualParams.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.h b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.h
index aa140874632..595fe8b52b7 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.h
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.h
@@ -23,7 +23,7 @@
 
 #include <sofa/component/mapping/nonlinear/config.h>
 
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.h>
 #include <sofa/component/mapping/nonlinear/NonLinearMappingData.h>
 #include <sofa/linearalgebra/EigenSparseMatrix.h>
 #include <sofa/core/topology/BaseMeshTopology.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.inl b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.inl
index 8e2a75fcdfe..a5b7d38ffd6 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.inl
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/DistanceMapping.inl
@@ -22,7 +22,7 @@
 #pragma once
 
 #include <sofa/component/mapping/nonlinear/DistanceMapping.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl>
 #include <sofa/core/BaseLocalMappingMatrix.h>
 #include <sofa/core/ConstraintParams.h>
 #include <sofa/core/MechanicalParams.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.h b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.h
index 423e4dea316..138c075f2ea 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.h
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.h
@@ -23,7 +23,7 @@
 
 #include <sofa/component/mapping/nonlinear/config.h>
 
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.h>
 #include <sofa/component/mapping/nonlinear/NonLinearMappingData.h>
 #include <sofa/linearalgebra/EigenSparseMatrix.h>
 #include <sofa/core/topology/BaseMeshTopology.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.inl b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.inl
index db6447dd0cb..d016ac706c1 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.inl
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareDistanceMapping.inl
@@ -22,7 +22,7 @@
 #pragma once
 
 #include <sofa/component/mapping/nonlinear/SquareDistanceMapping.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl>
 #include <sofa/core/BaseLocalMappingMatrix.h>
 #include <sofa/core/visual/VisualParams.h>
 #include <sofa/core/MechanicalParams.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.h b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.h
index 5c6dc7f701f..a8131b726bc 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.h
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.h
@@ -23,7 +23,7 @@
 
 #include <sofa/component/mapping/nonlinear/config.h>
 
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.h>
 #include <sofa/component/mapping/nonlinear/NonLinearMappingData.h>
 #include <sofa/linearalgebra/EigenSparseMatrix.h>
 
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.inl b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.inl
index 46486ce1493..970b25256c2 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.inl
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/SquareMapping.inl
@@ -22,7 +22,7 @@
 #pragma once
 
 #include <sofa/component/mapping/nonlinear/SquareMapping.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl>
 #include <sofa/core/BaseLocalMappingMatrix.h>
 #include <sofa/core/visual/VisualParams.h>
 #include <sofa/core/MechanicalParams.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.h b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.h
index debd8766eaa..7bb9ba22730 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.h
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.h
@@ -22,7 +22,7 @@
 #pragma once
 
 #include <sofa/component/mapping/nonlinear/config.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.h>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.h>
 #include <sofa/component/mapping/nonlinear/NonLinearMappingData.h>
 #include <sofa/core/topology/BaseMeshTopology.h>
 #include <sofa/linearalgebra/EigenSparseMatrix.h>
diff --git a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.inl b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.inl
index c3ce47d3479..899678361e4 100644
--- a/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.inl
+++ b/Sofa/Component/Mapping/NonLinear/src/sofa/component/mapping/nonlinear/VolumeMapping.inl
@@ -21,7 +21,7 @@
 ******************************************************************************/
 #pragma once
 #include <sofa/component/mapping/nonlinear/VolumeMapping.h>
-#include <sofa/component/mapping/nonlinear/AssembledNonLinearMapping.inl>
+#include <sofa/component/mapping/nonlinear/BaseNonLinearMapping.inl>
 #include <sofa/core/BaseLocalMappingMatrix.h>
 
 namespace sofa::component::mapping::nonlinear