diff --git a/Common/include/linear_algebra/CMatrixVectorProduct.hpp b/Common/include/linear_algebra/CMatrixVectorProduct.hpp
index 878bb132b98..a0cecaa63d7 100644
--- a/Common/include/linear_algebra/CMatrixVectorProduct.hpp
+++ b/Common/include/linear_algebra/CMatrixVectorProduct.hpp
@@ -72,6 +72,7 @@ class CSysMatrixVectorProduct final : public CMatrixVectorProduct<ScalarType> {
   const CSysMatrix<ScalarType>& matrix; /*!< \brief pointer to matrix that defines the product. */
   CGeometry* geometry;                  /*!< \brief geometry associated with the matrix. */
   const CConfig* config;                /*!< \brief config of the problem. */
+  mutable bool matrix_uploaded = false; /*!< \brief Upload the matrix lazily on the first actual GPU matvec. */
 
  public:
   /*!
@@ -97,6 +98,10 @@ class CSysMatrixVectorProduct final : public CMatrixVectorProduct<ScalarType> {
   inline void operator()(const CSysVector<ScalarType>& u, CSysVector<ScalarType>& v) const override {
     if (config->GetCUDA()) {
 #ifdef HAVE_CUDA
+      if (!matrix_uploaded) {
+        matrix.HtDTransfer();
+        matrix_uploaded = true;
+      }
       matrix.GPUMatrixVectorProduct(u, v, geometry, config);
 #else
       SU2_MPI::Error(
diff --git a/Common/src/linear_algebra/CSysMatrixGPU.cu b/Common/src/linear_algebra/CSysMatrixGPU.cu
index 90389264ed3..7e0c81ca54f 100644
--- a/Common/src/linear_algebra/CSysMatrixGPU.cu
+++ b/Common/src/linear_algebra/CSysMatrixGPU.cu
@@ -70,7 +70,6 @@ void CSysMatrix<ScalarType>::GPUMatrixVectorProduct(const CSysVector<ScalarType>
    ScalarType* d_vec = vec.GetDevicePointer();
    ScalarType* d_prod = prod.GetDevicePointer();
 
-   HtDTransfer();
    vec.HtDTransfer();
    prod.GPUSetVal(0.0);