Physical Sciences and Mathematics Commons^™

Contributions To The Solution Of Large Nonlinear Systems Via Model-Order Reduction And Interval Constraint Solving Techniques, Leobardo Valera

Open Access Theses & Dissertations

Many engineering problems boil down to solving partial differential equations (PDEs) that describe real-life phenomena. Nevertheless, efficiently and reliably solving such problems constitutes a major challenge in computational sciences and in engineering in general.

PDE-based systems can reach sizes so large after they are discretized. The large size in these problems generate several issues, among them we can mention: large space of storing, computing time, and the most important, lost of accuracy. A popular approach to solving such problems is assume that the PDE's solution is in a subspace, and the solution is sought there. This assumption and later searching …