Related to a rather broad scope of applications, there is a need for correspondingly diverging specializations. The University of Twente’s Applied Mathematics specialization ‘Mathematical systems theory, applied analysis and computational science’ is a unique combination of both fundamental and applied aspects of mathematics.

## COMBINATION OF SCIENTIFIC FIELDS

This specialization is provided by the following research groups:

### APPLIED ANALYSIS (AA)

Our research deals with the combination of modeling, analysis and simulation of problems from the natural, life and technical sciences. Typically, the models are expressed in partial differential equations, and methods from the Calculus of Variations and Dynamical System Theory for infinite dimensional systems are presently used most to study the models obtained from direct and inverse modeling. Computational / numerical algorithms are adapted and advanced as required by the application problem. Currently our application areas are in the fields of mathematical neuroscience and medical imaging.

Find out more on the AA-website

### HYBRID SYSTEMS (HS)

Systems, signals and control theory is an area of research that has roots in electrical engineering, mechanical engineering and mathematics, but also has applications in, for example, econometrics, process technology and computer science. An essential part of this area forms the study of coupled processes -- the dynamical behavior of the components and their interaction with each other and their environment. Besides the analysis of such systems, the problem often concerns the design of components in such a way that the interconnected system has certain desired properties such as stability or optimality. Problems of this type occur for example when we need to control the position of satellites or want to filter relevant information about the structure of earth layers from a seismic signal.

More information can be found on the HS-website

### MATHEMATICS OF COMPUTATIONAL SCIENCE (MACS)

Our Science group focuses on the mathematical aspects of advanced scientific computing. The two main research areas are

1. the development, analysis and application of numerical algorithms for the (adaptive) solution of partial differential equations

2. the mathematical modeling of multi-scale problems making these accessible for computation

Special emphasis is put on the development and analysis of discontinuous Galerkin finite element methods and efficient (parallel) solution algorithms for large algebraic systems.

Important applications are in the fields of computational electromagnetics (nanophotonics), free surface flows (water waves, inkjet printing), (dispersed) two-phase flows and phase transition, and granular flows.

More information can be found on the MACS-website

### MULTISCALE MODELING AND SIMULATION (MMS)

Our research group focuses on the mathematical development and application of computational models for complex physics acting simultaneously at micro- and macro scales.

We develop numerical methods and compatible model reduction techniques for partial differential equations from a fundamental and an applied perspective.

Main application areas are in

- mulitphase flows and phase transitions
- biomedical flows and tissue engineering
- self-organizing nano system

supported by research in: space-time parallel simulation, immersed boundary methods, compatible finite volume and spectral element discretisation.

More information can be found on the MMS-website