diff --git a/MathLib/LinAlg/GlobalMatrixVectorTypes.h b/MathLib/LinAlg/GlobalMatrixVectorTypes.h
index 4dafd718ddf9692cbf35c182129243c12561e43b..a3ddae379717880c8ecbe86806d647dff92fcff1 100644
--- a/MathLib/LinAlg/GlobalMatrixVectorTypes.h
+++ b/MathLib/LinAlg/GlobalMatrixVectorTypes.h
@@ -21,66 +21,45 @@
     #include "MathLib/LinAlg/Eigen/EigenVector.h"
     #include "MathLib/LinAlg/EigenLis/EigenLisLinearSolver.h"
 
-    namespace detail
-    {
-    using GlobalVectorType = MathLib::EigenVector;
-    using GlobalMatrixType = MathLib::EigenMatrix;
+    using GlobalVector = MathLib::EigenVector;
+    using GlobalMatrix = MathLib::EigenMatrix;
 
-    using LinearSolverType = MathLib::EigenLisLinearSolver;
-    }
+    using GlobalLinearSolver = MathLib::EigenLisLinearSolver;
 
 #elif defined(USE_PETSC)
     #include "MathLib/LinAlg/PETSc/PETScVector.h"
     #include "MathLib/LinAlg/PETSc/PETScMatrix.h"
     #include "MathLib/LinAlg/PETSc/PETScLinearSolver.h"
-namespace detail
-{
-    using GlobalVectorType = MathLib::PETScVector;
-    using GlobalMatrixType = MathLib::PETScMatrix;
 
-    using LinearSolverType = MathLib::PETScLinearSolver;
-}
+    using GlobalVector = MathLib::PETScVector;
+    using GlobalMatrix = MathLib::PETScMatrix;
 
-#else
-#ifdef OGS_USE_EIGEN
+    using GlobalLinearSolver = MathLib::PETScLinearSolver;
+
+#elif defined(OGS_USE_EIGEN)
     #include "MathLib/LinAlg/Eigen/EigenVector.h"
     #include "MathLib/LinAlg/Eigen/EigenMatrix.h"
     #include "MathLib/LinAlg/Eigen/EigenLinearSolver.h"
-namespace detail
-{
-    using GlobalVectorType = MathLib::EigenVector;
-    using GlobalMatrixType = MathLib::EigenMatrix;
-
-    using LinearSolverType = MathLib::EigenLinearSolver;
-}
-#else   // OGS_USE_EIGEN
-    #include "MathLib/LinAlg/Dense/DenseVector.h"
-    #include "MathLib/LinAlg/Dense/GlobalDenseMatrix.h"
-    #include "MathLib/LinAlg/Solvers/GaussAlgorithm.h"
-namespace detail
-{
-    using GlobalVectorType = MathLib::DenseVector<double>;
-    using GlobalMatrixType = MathLib::GlobalDenseMatrix<double>;
-
-    using LinearSolverType =
-        MathLib::GaussAlgorithm<GlobalMatrixType, GlobalVectorType>;
-}
-
-#endif    // USE_LIS
+
+    using GlobalVector = MathLib::EigenVector;
+    using GlobalMatrix = MathLib::EigenMatrix;
+
+    using GlobalLinearSolver = MathLib::EigenLinearSolver;
+
 #endif    // OGS_USE_EIGEN
 
 
 /// A type used for indexing of global vectors and matrices. It is equal to the
-/// GlobalMatrixType::IndexType and the GlobalVectorType::IndexType.
-static_assert(std::is_integral<detail::GlobalMatrixType::IndexType>::value,
+/// GlobalMatrix::IndexType and the GlobalVector::IndexType.
+static_assert(std::is_integral<GlobalMatrix::IndexType>::value,
               "The index type for global matrices is not an integral type.");
-static_assert(std::is_integral<detail::GlobalVectorType::IndexType>::value,
+static_assert(std::is_integral<GlobalVector::IndexType>::value,
               "The index type for global vectors is not an integral type.");
-static_assert(std::is_same<detail::GlobalMatrixType::IndexType,
-                           detail::GlobalVectorType::IndexType>::value,
+static_assert(std::is_same<GlobalMatrix::IndexType,
+                           GlobalVector::IndexType>::value,
               "The global matrix and vector index types do not match.");
 // Both types are integral types and equal, define a single GlobalIndexType.
-using GlobalIndexType = detail::GlobalMatrixType::IndexType;
+using GlobalIndexType = GlobalMatrix::IndexType;
 
 using GlobalSparsityPattern = MathLib::SparsityPattern<GlobalIndexType>;
 
diff --git a/NumLib/NumericsConfig.h b/NumLib/NumericsConfig.h
index 607704beddb6f7644cfc37f443bd017302a5b8a7..a3738f299880198df0f0ca33a4cd0469367f11de 100644
--- a/NumLib/NumericsConfig.h
+++ b/NumLib/NumericsConfig.h
@@ -30,8 +30,8 @@ namespace detail
 {
 using GlobalVectorMatrixBuilderType =
         NumLib::VectorMatrixBuilder<
-            GlobalMatrixType,
-            GlobalVectorType>;
+            GlobalMatrix,
+            GlobalVector>;
 }
 
 //
@@ -51,7 +51,7 @@ using GlobalSetupType =
     NumLib::GlobalSetup<
         detail::GlobalVectorMatrixBuilderType,
         detail::GlobalExecutorType,
-        detail::LinearSolverType>;
+        GlobalLinearSolver>;
 
 
 //