Model-assisted effective large scale matrix computations

Model-assisted effective large scale matrix computations

Advanced mathematical models very often require the solution of (sequences of) large algebraic linear systems, whose numerical treatment should incorporate problem information in order to be computationally effective. For instance, matrices and vectors usually inherit crucial (e.g., spectral) properties of the underlying continuous operators. In this talk we will discuss a few examples where the performance of state-of-the-art iterative linear system solvers can be dramatically enhanced by exploiting these properties. Our presentation will focus on structured linear systems stemming from the numerical discretization of systems of partial differential equations, as well as of optimal control problems constrained by partial differential equations.