Parallel and scientific computing
Parallelism is here to stay! Today, most computers, from laptops to supercomputers, are based on so-called multicore architectures. Connecting many hundreds of powerful, and possibly heterogeneous, multicore nodes using a high-performance interconnect leads to truly massive parallel systems with a tremendous performance potential.
This evolution makes it possible to solve even more complex and large-scale computational problems in science and engineering. At the same time, there is an immense demand for new and improved scalable, efficient, and reliable numerical algorithms, library software and tools. This is essential, so that computations are carried out in a reasonable time and with the accuracy and resolution required.
Matrix computations are both fundamental and ubiquitous in the Computational Sciences, e.g. in the modelling and simulation of problems ranging from galaxies to nanoscale, and in real-time airline scheduling and medical imaging. Pages on the Internet is called the world ́s largest matrix computation of today – with a hyperlink matrix of n-by-n, with n > 20 billion.
Besides such large-scale problems, there are many challenging matrix computations in the design and analysis of linear control systems. Modeling interconnected systems (e.g. electrical circuits) and mechanical systems (e.g. multibody contact problems) can lead to descriptor systems. Periodic models arise in several practical applications, e.g. the control of rotating machinery. We are investigating how to exploit the inherent structure of several of the associated matrix problems.