Welcome to the web-page of the Croatian Science Foundation Project Grant #9345.
Project summary
Scientific discoveries and technological advances are increasingly based on numerical scientific computing, and often interwoven with the advances in the developments of numerical methods and computing machinery. In such development, sharp precision tools for scientific computing are essential, where the computing is just one part of a complex research interaction network, including mathematical modelling, functional-analytic considerations, discretization methods, numerical algorithms, and mathematical software development and its implementation on a state of the art hardware.
This proposal is focused on functional and numerical analysis of operator theoretic models of selected complex mechanical systems from mathematical physics and engineering, with particular emphasis on the development of numerical methods and robust algorithms for computing. Such operator theoretic models are particularly amenable to be treated algebraically in the context of efficient and robust computational procedures of modern numerical linear algebra. The themes include adaptive (interior penalty) discontinuous Galerkin method in the penalty based formulation of the model for the complex mechanical system (e.g. stent), and vibration analysis for powertrains (car industry). In a related topic of vibration control, we study distributed control using dynamic multipliers from the dissipativity theory. In the frequency domain, we consider the problems of system identification and model order reduction posed as problems of rational approximation in the Hardy space H2. For all considered problems, we devise numerical algorithms and identify core numerical linear algebra computational tasks for which we plan to develop robust algorithms. These include Arnoldi-type eigensolver for both linear and quadratic large scale eigenvalue problems, and high accuracy algorithms for structured matrices of paired Cauchy structure. All developed algorithms will be delivered also as high performance mathematical software.