# DUNE PDELab (2.8)

Here we show how to solve a linear system of equations originating from a PDE directly using ISTL instead of PDELab's abstractions.

Note that generally, we recommend going the all-PDELab route as explained in Solving a linear system within PDELab.

First, we assemble our residual as in Assembling a linear system from a PDE

as well as the system matrix we want to solve:

So far, these are data types provided by PDELab. We can access the underlying ISTL data types via

and the ISTL vectors or matrices behind a PDELab object via:

Now we can wrap our matrix in a LinearOperator object

and pass that into our desired solver along with a preconditioner of our choice.

Applying the solver now returns the solution of the defect problem, i.e. A*v=d.

**Definition:**solver.hh:46

Finally, we can subtract that from our initial guess to obtain the solution of A*x=b:

In the end, let's print the solution to console.

**Definition:**io.hh:86

Full example code: recipe-linear-system-solution-istl.cc