Printing-the-system-Matrix.md

+Debugging may require inspecting the system (Jacobian) matrix from time to time.
+
+The following example shows a possible way to achieve this for a staggered-grid free-flow problem:
+
+We add the output within the `solveLinearSystemImpl_` overload for `Dune::MultiTypeBlockMatrix` Jacobians in `newtonsolver.hh`:
+
+```c++
+    // ...
+    //  MultiTypeBlockMatrix is not supported for printing, needs to be converted first
+
+    // create the bcrs matrix the IterativeSolver backend can handle
+    const auto M = MatrixConverter<JacobianMatrix>::multiTypeToBCRSMatrix(A);
+
+    // get the new matrix sizes
+    const std::size_t numRows = M.N();
+    assert(numRows == M.M());
+
+    // create the vector the IterativeSolver backend can handle
+    const auto bTmp = VectorConverter<SolutionVector>::multiTypeToBlockVector(b);
+    assert(bTmp.size() == numRows);
+
+    // create a blockvector to which the linear solver writes the solution
+    using VectorBlock = typename Dune::FieldVector<Scalar, 1>;
+    using BlockVector = typename Dune::BlockVector<VectorBlock>;
+    BlockVector y(numRows);
+
+    /////// BEGIN PRINTING /////////////////////////////////////////////////////
+    static const bool printmatrix = getParam<bool>("Problem.PrintMatrix", false);
+
+    if (printmatrix)
+    {
+        static int counter = 0;
+        const auto rank = Dune::MPIHelper::getCollectiveCommunication().rank();
+
+        Dune::storeMatrixMarket(M, "matrix_" + std::to_string(rank) +  "_iter_" + std::to_string(counter) + ".log");
+        Dune::storeMatrixMarket(bTmp, "rhs_" + std::to_string(rank) +  "_iter_" + std::to_string(counter) + ".log");
+
+        ++counter;
+    }
+  /////// END PRINTING /////////////////////////////////////////////////////
+
+// ....
+```
+
+This will write out files for the matrix and the residual vector for each Newton iteration and each process.
+
+You may then compare files using, e.g., `kompare` or `meld`.
+
+Keep in mind that the `MatrixMarket`format uses indices starting with `1` instead of `0`.
+
+For rather small matrices, you may also directly print the output to the terminal, giving you a graphical impression of the structure:
+
+```c++
+Dune::printmatrix(std::cout, M, "", "", 10/*width*/, 2/*precision*/);
+```
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