We are six research fellows at the Institute of Mathematics: M.Sc. Atte Aalto, M.Sc. Antti Hannukainen, Dr. Ville Havu (Department of Applied Physics) , Dr. Teemu Lukkari, Dr. Jarmo Malinen (the head of the project), M.Sc. Pertti Palo.
We study problems in applied mathematics where both mathematical systems theory and numerical analysis play a relevant role.
System theory is concerned with the behaviour and control of input/output phenomena for dynamical systems. Our main interest lies in infinite-dimensional state space, interior point control, or boundary control systems that are typically defined by linear PDE's from practical applications. The connection to numerical analysis is evident: if there is a well-motivated model for some phenomenon, then there is an immediate need for solving it efficiently by computer.
For infinite-dimensional systems and associated control problems, numerical aspects have not received as much interest as there is potential. Conversely, addition of some control theory aspect to a classical numerical analysis problem will result in fresh and relevant research.
We study these problems from both theoretical and applied, even from an experimental point of view.
A wide class of linear dynamical models in engineering either conserve or dissipate energy. In applications, the control action can often be exerted only from the outside of a geometric domain. A functional analytic framework for such problems is the theory of conservative (or, more generally, dissipative) boundary control systems; see [1, 2, 3, 4] and the numerous classical references therein.
An important class of conservative/dissipative systems is given by transmission lines, that can be either acoustic or electric. Operator theory of nonstandard transmission lines and wave guides is a subject of ongoing research , , .
We consider spatial and temporal discretisation of conservative boundary control systems. In conservative control problems, it is useful to consider energy conservation after discretisation, too; see [8, 9, 10] for temporal and [11,12,13] for spatial discretisations. We search for stable discretisations of control problems for a large class of physical systems, ultimately encompassing all problems that can be described as a linear passive (or, conservative) system. Important areas of application include boundary controlled PDE's in acoustics (see, e.g., , ), mechanics, and electromagnetics.
We study the human vocal tract by analytic and numerical methods. Acoustics of the vowel production can be modelled by the wave equation that actually defines an input part of a conservative boundary control system; see . The aim of this research is to construct a numerical simulator (using the techniques described in [5, 6]) that can be used for phonetic research and (when coupled to muscle and tissue models) for planning oral and maxillofacial surgery. A flow-mechanical glottis model has been developed, see ,  and the recent [seminar slides].
The computations are carried out by Finite Element Method. The required anatomical data is obtained by MRI. During the imaging sequence, sound samples must be recorded in a exceptionally challenging environment by a special arrangement; see , , , and the recent [seminar slides]. For background in speech research, see .
Further related (and many unrelated) publications can be found in our private home pages.
Research contacts outside the Institute of Mathematics, TKK, include Prof. Paavo Alku (TKK), Dr. Daniel Aalto, Prof. Olli Aaltonen (University of Helsinki), Prof. Risto-Pekka Happonen (University of Turku), Prof. Jaromir Horacek (Academy of Sciences of the Czech Republic), Dr. Mikael Kurula (Åbo Akademi University), Prof. Unto Laine (TKK), Prof. Anders Lindquist (KTH), Dr. Jani Saunavaara (Turku University Central Hospital), Prof. Olof Staffans (Åbo Akademi University), Prof. Tomas Vampola (Czech Technical University), Dr. Martti Vainio (University of Helsinki), Prof. George Weiss (Imperial College), and Prof. Hans Zwart (University of Twente).