Order reduction of complex systems
Reference persons STEFANO GRIVET TALOCIA
Description Numerical modeling and simulation is essential for understanding the behavior of structures and systems in practically every branch of science and engineering. Unfortunately, complexity often prevents direct approaches, where the whole system is characterized using first-principle models (typically systems of partial differential equations) and then simulated on a suitable computer. As an example, the design flow of portable computing devices such as smartphones and tablets requires an accurate evaluation of transient electromagnetic field, voltages and currents over a region characterized by an extremely complex geometry and by complicated material properties. This task is prohibitive using a direct full-system approach. Other examples may be vibration models for mechanical or aeronautical structures, and even behavioral models for biological structures such as the cardiovascular system.
Divide and conquer techniques have been demonstrated as excellent alternatives to break this complexity and perform numerical simulations in drastically reduced times. The overall system is first partitioned into well-defined sub-structures, which are characterized separately through approximate reduced-complexity behavioral models or "macromodels". These macromodels may be obtained by applying so-callsed Model Order Reduction (MOR) techniques to the large systems of ordinary differential equations arising from a spatial discretization of the fields in the domain of interest. Once available, these models are cascaded to build an approximate yet accurate representation of the whole system, which can then be solved with limited computing resources.
This thesis is aimed at reviewing the most prominent MOR approaches, i.e., for the automatic approximation of the dynamic behavior of a large complex system with simple, compacts and low order models. Main objective will be the creation of a software package implementing the most important MOR techniques. The results of this activity will find application in several engineering disciplines. There are even opportunities for internships with industrial partners in the field of CAD/EDA (Computed Aided Design/Electronic Design Automation) and/or with leading semiconductor companies.
Required skills Basic knowledge of numerical analysis. Good programming skills, Matlab language. Interest and skill in applied mathematics.
Deadline 01/02/2024 PROPONI LA TUA CANDIDATURA