Davide Palitta: Large-scale linear matrix equations and application to the numerical solution of elliptic PDEs

We are interested in the numerical treatment of large-scale linear matrix equations stemming from the discretization of elliptic PDEs on regular domains and uniform meshes. In the first part of this seminar, we introduce (multiterm) linear matrix equations, the way they arise in the finite difference discretization of 2D and 3D convection-diffusion partial differential equations with separable coefficients. We discuss available numerical solution methods for these matrix equations, an in particular we present new preconditioning strategies that rely on solving Sylvester matrix equations. Moreover, we present effective computational modifications that are applicable when the coefficient matrices are symmetric. Several numerical results illustrate the potential of the proposed strategies, showing that this methodology may represent a valuable alternative to well established standard linear system solvers.