diff --git a/MathLib/LinAlg/PETSc/PETScVector.cpp b/MathLib/LinAlg/PETSc/PETScVector.cpp
index a23f072be7029d505fa185fae3ecc7cf23ca87bb..52415470112ec59d900e6fc9d55dd6083655e8e5 100644
--- a/MathLib/LinAlg/PETSc/PETScVector.cpp
+++ b/MathLib/LinAlg/PETSc/PETScVector.cpp
@@ -44,8 +44,9 @@ PETScVector::PETScVector(const PetscInt vec_size, const bool is_global_size)
 
 PETScVector::PETScVector(const PetscInt vec_size,
                          const std::vector<PetscInt>& ghost_ids,
-                         const bool is_global_size) :
-                         _size_ghosts(ghost_ids.size()), _has_ghost_id(true)
+                         const bool is_global_size)
+    : _size_ghosts{ghost_ids.size()}
+    , _has_ghost_id{true}
 {
     _v.reset(new PETSc_Vec);
 
@@ -77,6 +78,17 @@ PETScVector::PETScVector(const PETScVector &existing_vec, const bool deep_copy)
     }
 }
 
+PETScVector::PETScVector(PETScVector &&other)
+    : _v{std::move(other._v)}
+    , _v_loc{std::move(other._v_loc)}
+    , _start_rank{other._start_rank}
+    , _end_rank{other._end_rank}
+    , _size{other._size}
+    , _size_loc{other._size_loc}
+    , _size_ghosts{other._size_ghosts}
+    , _has_ghost_id{other._has_ghost_id}
+{}
+
 void PETScVector::config()
 {
     VecSetFromOptions(*_v);
@@ -232,10 +244,12 @@ void PETScVector::shallowCopy(const PETScVector &v)
 
     VecDuplicate(*v._v, _v.get());
 
-    // TODO can't that be copied from v?
-    VecGetOwnershipRange(*_v, &_start_rank,&_end_rank);
-    VecGetLocalSize(*_v, &_size_loc);
-    VecGetSize(*_v, &_size);
+    _start_rank   = v._start_rank;
+    _end_rank     = v._end_rank;
+    _size         = v._size;
+    _size_loc     = v._size_loc;
+    _size_ghosts  = v._size_ghosts;
+    _has_ghost_id = v._has_ghost_id;
 
     VecSetOption(*_v, VEC_IGNORE_NEGATIVE_INDICES, PETSC_TRUE);
 }
diff --git a/MathLib/LinAlg/PETSc/PETScVector.h b/MathLib/LinAlg/PETSc/PETScVector.h
index bf3f4e46f630c6708bf7baf30c96a8a27c754be0..ce15cbe8f4614dd990a96d24e8191f1644bfe091 100644
--- a/MathLib/LinAlg/PETSc/PETScVector.h
+++ b/MathLib/LinAlg/PETSc/PETScVector.h
@@ -72,7 +72,9 @@ class PETScVector
              \param deep_copy    The flag for a deep copy, which means to copy the values as well,
                                  the default is true
         */
-        PETScVector(const PETScVector &existing_vec, const bool deep_copy = true);
+        explicit PETScVector(const PETScVector &existing_vec, const bool deep_copy = true);
+
+        PETScVector(PETScVector&& other);
 
         ~PETScVector()
         {
@@ -221,12 +223,19 @@ class PETScVector
         void setZero() { *this = 0.0; }
 
         /// Overloaded operator: assign
-        void operator = (const PETScVector &v_in)
+        PETScVector& operator = (const PETScVector &v_in)
         {
             if (!_v) shallowCopy(v_in);
             VecCopy(*v_in._v, *_v);
+
+            return *this;
         }
 
+        /// Disallow moving.
+        /// \todo This operator should be implemented properly when doing a
+        ///       general cleanup of all matrix and vector classes.
+        PETScVector& operator = (PETScVector &&) = delete;
+
         ///  Overloaded operator: add
         void operator += (const PETScVector& v_in)
         {
diff --git a/NumLib/ODESolver/MatrixTranslator.h b/NumLib/ODESolver/MatrixTranslator.h
index 6df68880311403152646c2f83cc466a9d4e055a7..76970880311f22f24b019df4123cc7bef0d026c2 100644
--- a/NumLib/ODESolver/MatrixTranslator.h
+++ b/NumLib/ODESolver/MatrixTranslator.h
@@ -404,7 +404,7 @@ public:
         // Note: using x_old here is correct, since this method is called from within
         //       CrankNicolson::pushState() __after__ x_old has been updated to the result
         //       from the timestep just finished.
-        auto const x_old = _crank_nicolson.getXOld();
+        auto const& x_old = _crank_nicolson.getXOld();
 
         // _M_bar = (1.0-theta) * M;
         BLAS::copy(M, _M_bar);
diff --git a/NumLib/ODESolver/TimeLoopSingleODE.h b/NumLib/ODESolver/TimeLoopSingleODE.h
index dd69d77269297970ae877de696844827705db139..ff8f29d8e086bda2b65dc8b9b7c5fbfaff4f6a36 100644
--- a/NumLib/ODESolver/TimeLoopSingleODE.h
+++ b/NumLib/ODESolver/TimeLoopSingleODE.h
@@ -64,7 +64,7 @@ public:
      * \retval false otherwise
      */
     template<typename Callback>
-    bool loop(const double t0, const Vector x0,
+    bool loop(const double t0, Vector const& x0,
               const double t_end, const double delta_t,
               Callback& post_timestep);
 
@@ -81,7 +81,7 @@ template<typename Matrix, typename Vector, NonlinearSolverTag NLTag>
 template<typename Callback>
 bool
 TimeLoopSingleODE<Matrix, Vector, NLTag>::
-loop(const double t0, const Vector x0, const double t_end, const double delta_t,
+loop(const double t0, Vector const& x0, const double t_end, const double delta_t,
      Callback& post_timestep)
 {
     // solution vector