Multiphysics problems considered in this lecture series are those that can be described by mathematical models relying on different kind of partial differential equations. As a guiding principle, the numerical approximation of partial differential equations governing these problems can take advantage of domain decomposition (DD) methods. In the first part of this presentation we will introduce a general mathematical setting for DD, discuss DD preconditioners, and illustrate their role and efficiency for parallel computing. In the second part, we will address numerical strategies for complexity reduction in multiphysics problems. These strategies can be based on the attempt of simplifying the original mathematical model, devising novel numerical approximation methods, developing efficient parallel algorithms that exploit the dimensional reduction paradigm. After introducing some illustrative examples, several approaches will be proposed and a few representative applications to medicine, sports design, and the environment will be addressed.

Professor: Alfio Quarteroni École Polytechnique Fédéral de Lausanne (Switzerland) /Politecnico di Milano (Italy).

Register: It's free. Registration would be appreciated before July 12 (elisa.eiroa @ usc.es)
Credits: Both courses are equivalent to a credit in the doctoral program "Mathematical Methods and Numerical Simulation in Engineering and Applied Science".