Research

The main focus is on mathematical modelling in engineering. However, theoretically oriented research in analysis and stochastics and practical research in biomechanics is undertaken as well.

The two main research subjects of the unit are:


Partial differential equations and dynamical systems.

The research topics comprise:

  • Generalized solutions to nonlinear partial differential equations, propagation of singularities in linear partial differential equations with discontinuous coefficients, stochastic partial differential equations, algebras of generalized functions, Fourier integral operators. → Michael Oberguggenberger
  • Inverse problems, ill-posed problems, imaging and optimization, kinetic theory and statistical mechanics, shock and delta wave solutions to quasilinear hyperbolic systems. →  Lukas Neumann
  • Linear partial differential equations and systems, fundamental solutions and Green's functions, linear theory of generalized functions, functional analysis. → Peter Wagner
  • Multibody simulations, coupled systems of ordinary and partial differential equations. → Robert Eberle


In all these fields, contributions cover theory (development of new mathematical concepts and methods) and applications in physics and in the engineering sciences, especially in elasticity.


Stochastic, probabilistic and generalized probabilistic methods. 

The research topics cover the development of new mathematical methods and applications in engineering sciences, risk analysis, operations research and biomechanics. They comprise:

  • Classical probabilistic methods and Monte-Carlo simulation.
  • Imprecise probabilities such as families of probability measures or random sets.
  • Non-probabilistic methods using intervals and fuzzy sets.

Learn more  ...

Robert Eberle, Thomas Fetz, Michael Oberguggenberger


 

The unit is well imbedded in the international research communities in the mentioned fields. The unit is also actively engaged in the research center Computational Engineering. An additional important activity of the unit is advice and consultations of other units of the faculty on mathematical questions arising in engineering research. The resulting collaboration frequently leads to joint publications. Traditionally, the unit’s research has been funded by the Austrian Science Fund (FWF). In recent years collaboration with industrial partners has been intensified, which resulted in a number of research projects financed by the Austrian Research Promotion Agency (FFG) as well as third-party funded industrial projects.

Some typical examples of recent research results include: wave propagation in discontinuous continua [1], multibody simulations with stochastic effects [2], imprecise probability and Monte Carlo simulation with applications in reliability [3], inverse problems and optimization [4], strongly singular solutions in the systems of gas kinetics [5].

[1]  Deguchi, M. Oberguggenberger, Propagation of singularities for generalized solutions to wave equations with discontinuous coefficients. SIAM J. Math. Analysis 48 (2016), 397-442, https://doi.org/10.1137/15M1032661.

[2]  Eberle, P. Kaps, M. Oberguggenberger, A multibody simulation study of alpine ski vibrations caused by random slope roughness. Journal of Sound and Vibration 446 (2019), 225-237, https://doi.org/10.1016/j.jsv.2019.01.035.

[3]  Fetz, M. Oberguggenberger: Imprecise random variables, random sets, and Monte Carlo simulation. International Journal of Approximate Reasoning 78 (2016), 252-264, http://dx.doi.org/10.1016/j.ijar.2016.06.012.

[4]  Rabanser, L. Neumann, M. Haltmeier, Analysis of the Block Coordinate Descent Method for Linear Ill-Posed Problems. SIAM Journal on Imaging Sciences 12/4 (2019), 1808-1832, https://doi.org/10.1137/19M1243956.

[5]  M. Nedeljkov, L. Neumann, M. Oberguggenberger, M. R. Sahoo, Radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions. Nonlinear Analysis 163 (2017), 104-126, https://doi.org/10.1016/j.na.2017.07.006

 

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