"Subspace Recycling for Sequences of Linear Systems" Prof. Eric de Sturler Department of Mathematics, 460 McBryde Hall, Virginia TechBlacksburg, VA 24061-0123, USA
In many computational science and engineering problems, we have to solve a sequence of large, sparse, linear systems, in which the matrix changes slowly from one system to the next or changes in an algebraically structured way. The right hand side can change more drastically, although in many applications this is not the case. We have developed several methods that significantly improve the convergence of iterative solvers by recycling from one system to the next a judiciously selected subspace of the search space, for example an approximate invariant subspace, but other possibilities have proven effective as well.
We will discuss the underlying mathematics of iterative solvers and for recycling search spaces in iterative solvers, a number of applications and results, and a convergence theory for recycling approximate invariant subspaces. Using the latter we demonstrate that significant convergence improvements can be achieved with very modest accuracy.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
