The seminar will take place on Monday, February 19, 2018 at 9:00 am in K4. Prof. Zdeněk Strakoš will present the next part of the lecture “Decomposition into subspaces and operator preconditioning”.
Abstract: We will consider linear equations in the abstract infinite-dimensional Hilbert space setting with bounded, coercive and self-adjoint operators, which can represent, e.g., boundary value problems formulated via partial differential equations.
Efficient numerical solution procedures often incorporate transformation of the original problem using preconditioning. Motivated, in particular, by the works of Faber, Manteuffel, Parter, Oswald, Dahmen, Kunoth and Rude published in the early 90’s, we will present an abstract formulation of operator preconditioning based on the idea of decomposition of a Hilbert space into a finite number of (infinite-dimensional) subspaces, by formulating the main results using the concepts of norm equivalence and spectral equivalence of infinite-dimensional operators. Its goal is to describe in a concise way the common principles behind various adaptive multilevel and domain decomposition techniques using infinite-dimensional function spaces.