Several recently developed model order reduction methods for fast simulation of large-scale dynamical systems with two or more parameters are reviewed. Besides, an alternative approach for linear parameter system model reduction as well as a more efficient method for nonlinear parameter system model reduction are proposed in this paper. Comparison between different methods from theoretical eleg...

with input u(t) ∈ Rm, state x(t) ∈ RN and output y(t) ∈ Rp. Without loss of generality, we can assume that the system is controllable and observable since otherwise we can always find a smaller dimensional model that is controllable and observable, and that has exactly the same transfer function. In addition to this, we will assume that the system is stable, i.e. the generalized eigenvalues of ...

In the initial stages of refining a mathematical model of a real-world dynamical system, one is often confronted with many more variables and coupled differential equations than one intuitively feels should be sufficient to describe the system. Yet none of the variables may seem so irrelevant as to be excludable nor so dominant as to explain the overall dynamics. Part of the problem might even ...

This paper considers the problem of H2 reduced order approximation for both continuous and discrete time MIMO systems. A heuristic algorithm is proposed that utilizes necessary and sufficient conditions expressed in terms of a set of LMIs and a matrix rank constraint, and the alternating projection method. Also a method of finding starting points is suggested. Three numerical examples are emplo...

This paper discusses procedures for approximating high-order rational Dower spectrum matrices and minimum ~ h a s e stable transfer function matrices by lower-order objects of the same type. The basis of the approximation is to secure closeness of a high-order and low-order minimum phase stable transfer function matrix in phase, and to infer from this, closeness in magnitude. A suitable definit...

In this contribution we present efficient numerical multiscale methods for flow in heterogeneous porous media, in particular also in situations where the resulting equations are to be solved repeatedly for varying parameters, as e.g. in the context of uncertainty quantification, time dependent scenarios or optimal control problems. We discuss a posteriori based discretization methods and sugges...

|Abstract: High-Technological solutions of today are characterized by complex dynamical models. A lot of these models have inherent hybrid/switching structure. Hybrid/switched systems are powerful models for distributed embedded systems design where discrete controls are applied to continuous processes. Hybrid systems are also an important modeling class for nonlinear systems because a wide var...

In this first section we present a high level discussion on computational science, and the need for compact models of phenomena observed in nature and industry. We argue that much more complex problems can be addressed by making use of current computing technology and advanced algorithms, but that there is a need for model order reduction in order to cope with even more complex problems. We als...

Methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equations are presented. Featured methods include the Chapman-Enskog expansion, Grad’s moment method, and the author’s order of magnitude method. The resulting macroscopic equations are compared and discussed by means of simple problems, including linear stability, shock wave structures, and Couette flow.